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1. Optimal Interpretability-Performance Trade-off of Classification Trees with Black-Box Reinforcement Learning

Author: Kohler, Hector, Akrour, Riad, Preux, Philippe, Scool (Scool), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université de Lille, Centrale Lille, Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille Nord Europe - Laboratoire CRIStAL - Université de Lille, Scool [Scool], and Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Subjects: Reinforcement Leaning, Supervised Learning, Interpretability, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: Interpretability of AI models allows for user safety checks to build trust in these models. In particular, decision trees (DTs) provide a global view on the learned model and clearly outlines the role of the features that are critical to classify a given data. However, interpretability is hindered if the DT is too large. To learn compact trees, a Reinforcement Learning (RL) framework has been recently proposed to explore the space of DTs. A given supervised classification task is modeled as a Markov decision problem (MDP) and then augmented with additional actions that gather information about the features, equivalent to building a DT. By appropriately penalizing these actions, the RL agent learns to optimally trade-off size and performance of a DT. However, to do so, this RL agent has to solve a partially observable MDP. The main contribution of this paper is to prove that it is sufficient to solve a fully observable problem to learn a DT optimizing the interpretability-performance trade-off. As such any planning or RL algorithm can be used. We demonstrate the effectiveness of this approach on a set of classical supervised classification datasets and compare our approach with other interpretability-performance optimizing methods.
Published: 2023

2. MLGL: An R Package Implementing Correlated Variable Selection by Hierarchical Clustering and Group-Lasso

Author: Grimonprez, Quentin, Blanck, Samuel, Celisse, Alain, Marot, Guillemette, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), We thank Direction Générale de l’Armement (DGA) and Inria for a financial support of Quentin Grimonprez’s PhD, and the CPER Nord-Pas de Calais/FEDER DATA Advanced data science and technologies 2015-2020., Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Marot, Guillemette
Subjects: Mathematical statistics, group selection, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], correlated variables, penalized regression, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], hierarchical clustering
Abstract: International audience; The MLGL R-package, standing for Multi-Layer Group-Lasso, implements a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high dimensional data. A sparsity assumption is made that is, only a few variables are assumed to be relevant for predicting the response variable. In this context, the performance of classical Lasso-based approaches strongly deteriorates as the redundancy strengthens. The proposed approach combines variables aggregation and selection in order to improve interpretability and performance. First, a hierarchical clustering procedure provides at each level a partition of the variables into groups. Then, the set of groups of variables from the different levels of the hierarchy is given as input to group-Lasso, with weights adapted to the structure of the hierarchy. At this step, group-Lasso outputs sets of candidate groups of variables for each value of regularization parameter. The versatility offered by MLGL to choose groups at different levels of the hierarchy a priori induces a high computational complexity. MLGL however exploits the structure of the hierarchy and the weights used in group-Lasso to greatly reduce the final time cost. The final choice of the regularization parameter – and therefore the final choice of groups – is made by a multiple hierarchical testing procedure.
Published: 2023

3. Optimistic Dynamic Regret Bounds

Author: Haddouche, Maxime, Guedj, Benjamin, Wintenberger, Olivier, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Machine Learning (stat.ML), Mathematics - Optimization and Control, Machine Learning (cs.LG)
Abstract: Online Learning (OL) algorithms have originally been developed to guarantee good performances when comparing their output to the best fixed strategy. The question of performance with respect to dynamic strategies remains an active research topic. We develop in this work dynamic adaptations of classical OL algorithms based on the use of experts' advice and the notion of optimism. We also propose a constructivist method to generate those advices and eventually provide both theoretical and experimental guarantees for our procedures.
Published: 2023

4. Hybrid Kinetic/Fluid numerical method for the Vlasov-BGK equation in the diffusive scaling

Author: Laidin, Tino, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Reliable numerical approximations of dissipative systems (RAPSODI ), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-17-CE40-0027,MoHyCon,Modèles multi-échelles et simulation numérique hybride de semi-conducteurs(2017), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe
Subjects: Kinetic equations, Hybrid solver, 65M08, 82M12, 35B40, 65M55, Micro-macro decomposition, FOS: Mathematics, Diffusion scaling, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Asymptotic preserving scheme
Abstract: This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of the asymptotic fluid model while reducing the error induced by the latter approach. It relies on two criteria motivated by a pertubative approach to obtain a dynamic domain decomposition. The first criterion quantifies how far from a local equilibrium in velocity the distribution function of particles is. The second one depends only on the macroscopic quantities that are available on the whole computing domain. Interface conditions are dealt with using a micro-macro decomposition and the method is significantly more efficient than a standard full kinetic approach. Some properties of the hybrid method are also investigated, such as the conservation of mass., 31 pages, 20 figures, 6 Tables
Published: 2023

5. Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation

Author: Lorenzo Pareschi, Thomas Rey, Department of Mathematics [Ferrara], Università degli Studi di Ferrara = University of Ferrara (UniFE), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-17-CE40-0027,MoHyCon,Modèles multi-échelles et simulation numérique hybride de semi-conducteurs(2017), Università degli Studi di Ferrara (UniFE), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, and Centre National de la Recherche Scientifique (CNRS)-Université de Lille
Subjects: Numerical Analysis, Fourier-Galerkin spectral method, Applied Mathematics, MSC 76P05, 65N35, 82C40, Numerical Analysis (math.NA), stability, spectral accuracy, Maxwellian equilibrium, Boltzmann equation, Computational Mathematics, FOS: Mathematics, Mathematics - Numerical Analysis, conservative methods, [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can lead to the wrong long time behavior of the numerical solution. We introduce in this paper a novel Fourier-Galerkin spectral method that improves the classical spectral method by making it conservative on the moments of the approximated distribution, without sacrificing its spectral accuracy or the possibility of using fast algorithms. The method is derived directly using a constrained best approximation in the space of trigonometric polynomials and can be applied to a wide class of problems where preservation of moments is essential. We then apply the new spectral method to the evaluation of the Boltzmann collision term, and prove spectral consistency and stability of the resulting Fourier-Galerkin approximation scheme. Various numerical experiments illustrate the theoretical findings., Comment: 25 pages, 1 table, 3 figures
Published: 2022

6. The Patient Path: a first approach

Author: Essifi, Rim, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Équipe MODAL, Projet PATH, and Essifi, Rim
Subjects: care pathways, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], longitudinal data analysis, Gaussian processes, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], functional data analysis, clustering
Abstract: International audience; European healthcare systems are faced with multiple challenges, including anaging population, an increase in chronic diseases and patients withmulti-morbidity, and limited financial and human resources. The response tothese challenges is based in particular on the organisation of care into carepathways. Namely, Once the data necessary for the construction of a carepathway are acquired and processed, one has to model the patient pathwaymathematically in a generic way. After that, using clustering algorithms, one canidentify patients subgroups, then, mine for common treatments, predict thefuture of patient pathways and answer clinicians’ questions. All these steps wouldlead to an automated processes which has to be evaluated by medical experts.Available statistical methods remain limited and inefficient to construct carepathways. Indeed, data obtained from health care providers and insurancecompanies are all time-dependent, highly heterogeneous, qualitative in part, withseveral thousand possible modalities and mainly made up of missing data. Wepropose an approach based on functional data analysis combined withlongitudinal data analysis in order to construct care pathways.
Published: 2022

7. Reporting Context Aware Partial Translation engine based on immediate and delayed Rule application

Author: Bragagnolo, S. (Santiago), Ducasse, S. (Stephane), Anquetil, N. (Nicolas), Seriai, A. (Abderrahmane), Derras, M. (Mustapha), Université de Lille, Centre National de la Recherche Scientifique (CNRS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), Centrale Lille, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Berger-Levrault, INRIA Lille - Nord Europe, and Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Subjects: Incremental, Refactor, Migration Iterative Incremental Context-Aware Microservice Monolith Standalone Software Evolution Refactor, Standalone, Software Evolution, Microservice, Monolith, Migration, Iterative, Context-Aware, [INFO]Computer Science [cs]
Abstract: Language migration has been the driver of many efforts resulting in multiple solutions and strategies. One of the most popular approaches for dealing with it is source code translation: it proposes to translate the source code of an application to a target language. For doing so it leverages a set of translation rules based on the grammatical constructions provided by the source and target languages. However, we notice that even when most of the literature acknowledges translating implies migrating the runtime, libraries and the Software Development Kit (SDK), none of them proposes a systematic way to solve this problem. Along with this, we notice that there are many proposals to shift the paradigm from procedural to object-oriented programming based on how to propose classes automatically. But we found nothing on how to translate the expressions that use functions into expressions that use methods. In the context of migration from Microsoft Access (MS Access) to web technologies, these two lacks threaten seriously any attempt to produce even a compilable version of the code on the target technology. This article proposes a translation engine that split the translation process into two phases. A phase of language translation, and a phase of adaptation to the target environment. The first phase is in charge of producing declarations, and the second one is in charge of adapting the usage of this declaration to fit the translated version of our artefacts. We argue that enabling to adapt the code to fit the translated version of our artefacts allows the definition of simple adapting rules able to deal with a large share of both problems: (i) runtime, libraries and the Software Development Kit (SDK), and (ii) simple paradigm shift. This article presents some basic adapting rules and validates our approach by translating a battery of simple tests that feature the usage of a carefully chosen set of features.
Published: 2022

8. Efficient iterative methods for clustering and matching problems on graphs

Author: Braun, Guillaume, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Université de Lille, Christophe Biernacki, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), and Hemant Tyagi (co-encadrant)
Subjects: SBM, classification, Graph clustering, Power method, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], iterative methods, méthodes itératives, Graph matching, Alignement de graphes, Modèle à blocs stochastiques, clustering, Méthode de la puissance généralisée
Abstract: Graph structured datasets arise naturally in many fields including biology with protein-to-protein interaction networks, ecology with predator-prey networks and economy with financial market networks. In order to extract relevant information from these networks, one often uses clustering methods to gather nodes having similar connectivity patterns into communities. Numerous clustering algorithms have been proposed in the past decade and have been analyzed under the Stochastic Block Model (SBM), a popular random graph model. However, in practice, one often has access to side information, and it is typically unclear how this information can be incorporated in existing methods and to what extent it can help to improve the clustering performance.We will first address this question under the Contextual SBM (CSBM) -- a simple extension of the SBM with independent Gaussian covariates associated to each nodes -- and propose an iterative refinement method that is fast and achieves the information theoretic threshold for exact recovery. Our method is inspired by the Generalized Power Method (GPM) and principles of EM type algorithms.Next, we extend the method in order to be applied to networks with heterogeneous degrees or mixed-membership, but also with different kind of covariates like multilayer graphs with possibly missing values, or high dimensional bipartite graphs, hence showing the flexibility of the approach.Lastly, we consider the graph matching problem where the additional graphs can be considered as correlated side information. We show that we can also use the GPM for this problem to significantly improve the matching obtained by state-of-the art methods, and provide consistency guarantees for the GPM under the Correlated Wigner Model (CoWM).; Des données structurées sous forme de graphe apparaissent naturellement dans de nombreux domaines comme la biologie avec les réseaux d'interaction protéine-protéine, l'écologie avec les réseaux proie-prédateur ou l'économie avec les réseaux financiers. Afin d'extraire une information pertinente de ces réseaux, on a souvent recours à des méthodes de classification qui regroupent entre eux les nœuds ayant un profil de connectivité similaire. Durant les vingt dernières années, de nombreux algorithmes de classification ont été proposés et analysés lorsque le graphe est généré par un modèle à blocs stochastiques (SBM). Mais en pratique, on a souvent accès à de l'information auxiliaire. Il n'est toutefois pas bien compris comment cette information auxiliaire peut-être incorporée par les méthodes existantes, et dans quelle mesure elle peut aider à améliorer les résultats de la classification.Dans un premier temps nous allons résoudre ce problème en s'appuyant sur un modèle génératif simple - le modèle à blocs stochastiques contextuel (CSBM) - qui ajoute à chaque nœud d'un graphe généré par un SBM des covariables gaussiennes. Nous proposons une méthode itérative rapide qui atteint le seuil théorique d'information pour le recouvrement exact des communautés latentes. Notre méthode s'inspire de la méthode de la puissance généralisée (GPM) ainsi que des algorithmes de type EM.Nous étendons ensuite la méthode à des graphes ayant des nœuds avec des degrés hétérogènes ou appartenant à plusieurs communautés, ainsi qu'à des covariables de différentes natures, comme par exemple des réseaux multicouches avec des valeurs manquantes ou des graphes bipartites en grande dimension.Enfin, nous considérons le problème d'appariement de graphes dans lequel le graphe additionnel peut être considéré comme de l'information auxiliaire corrélée. Nous montrons que l'on peut également utiliser une stratégie basée sur GPM pour améliorer de manière significative un appariement initial imparfait. Nous établissons des garanties de consistance de l'algorithme sous le modèle de Wigner corrélé (CoWM).
Published: 2022

9. Éco-développement : une approche empirique pour réduire la consommation énergétique des logiciels

Author: Chakib, Mohammed, Self-adaptation for distributed services and large software systems (SPIRALS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Lille University, Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189, SPIRALS - Self-adaptation for distributed services and large software systems, Romain Rouvoy, and Lionel Seinturier
Subjects: Logiciels, [INFO.INFO-PL]Computer Science [cs]/Programming Languages [cs.PL], Économies d’énergie, Langages de programmation, java, [INFO.INFO-SE]Computer Science [cs]/Software Engineering [cs.SE], langage de programmation, Serveurs, green coding, python, servers, programming languages, energy consumption, energy measurement, datacenter, [INFO]Computer Science [cs], Centre de traitement informatique, Consommation d’énergie, Développement
Abstract: The ICT sector is claimed to account for 2% of global emissions. Even though this might seem like a small number, the success of ICT technologies will always lead to more greenhouse gas emissions. In 2019, the number of data centers worldwide was 1.5 million, which is expected to reach 2.5 million by 2025. In this situation, lowering the emissions from the ICT sector depends on reducing the amount of energy used by data centers. There are three main methods to achieve this goal: improving the hardware’s efficiency, lowering the cooling systems’ energy consumption, or decreasing the energy consumption of the servers themselves. This thesis focuses on the last approach, which I believe is the most affordable one, as it does not require any physical changes to data centers. My goal is to assist developers in making more eco-friendly software services by providing them with tools and guidelines to create software that runs on servers while consuming less energy. To do so, I decided to pursue an empirical approach consisting of three steps: test, measure, and optimize.The reason for such a decision is to follow the rapid pace of the software industry. In fact, the software industry has one of the fastest growth rates, which makes it challenging to keep up with the newest technologies. So, instead of just reporting my insights, I gave practitioners the means and protocols to allow them to test their hypotheses. I believe that some of the insights shared as part of this thesis might already have become obsolete when published.Due to the urgency of the climate change issue, I decided first to harness the most popular yet energy-hungry programming language, Python. Therefore, I started by analyzing Python’s code’s energy behavior during its most commonly used cases. Then, I provided a non-intrusive technique to reduce its energy consumption. After that, I extended this strategy to another programming language famous for its legacy code base, Java, to show that we can still reduce the energy consumption of already running applications without paying a considerable price.Finally, I adopted a more systemic approach. Instead of optimizing one single application, can one reduce the energy consumption of the data center as a whole entity? Thanks to the micro-services architecture, one application can be constructed using many services, each independent of the other. This type of architecture releases us from the bond of adopting a single programming language as the monolithic application does. And with this, one can use multiple programming languages and take advantage of the strengths of each one for a specific scenario. The last chapter analyzed the energy behavior of several programming languages regarding web services while opening a new path toward sustainability within timeless applications.; Le secteur des TIC serait responsable de 2% des émissions mondiales. Même si ce chiffre peut paraître faible, le succès des technologies TIC entraînera toujours une augmentation des émissions de gaz à effet de serre. En 2019, le nombre de centres de données dans le monde était de 1,5 million, et devrait atteindre 2,5 millions d’ici 2025. Dans cette situation, la diminution des émissions du secteur des TIC dépend de la réduction de la consommation énergétique des centres de données. Il existe trois méthodes principales pour atteindre cet objectif : améliorer l’efficacité du matériel, faire baisser la consommation énergétique des systèmes de refroidissement, ou diminuer la consommation énergétique des serveurs eux- mêmes. Cette thèse se focalise sur la dernière approche, qui me semble être la plus abordable, car elle ne nécessite aucun changement physique dans les centres de données.Mon objectif est d’aider les développeurs à créer des logiciels plus écologiques en leur fournissant des outils et des directives pour créer des applications qui tournent sur des serveurs tout en consommant moins d’énergie. Pour ce faire, j’ai décidé d’adopter une approche empirique en trois étapes : tester, mesurer et optimiser.La raison d’une telle décision est de suivre le rythme rapide de l’industrie du logiciel. En fait, le secteur du logiciel connaît l’un des taux de croissance les plus rapides, ce qui rend difficile de suivre les nouvelles technologies. Ainsi, au lieu de me contenter de rapporter juste mes réflexions, j’ai fourni aux praticiens les moyens et les protocoles nécessaires pour leur permettre de tester leurs hypothèses. Je suis convaincu que certaines des conclusions partagées dans le cadre de cette thèse pourraient déjà être obsolètes au moment de leur publication.Vue l’urgence de la question du changement climatique, j’ai décidé d’abord d’exploiter le langage de programmation le plus populaire et pourtant le plus gourmand en énergie, Python. J’ai donc commencé par analyser le comportement énergétique du code Python dans ses utilisations les plus courantes. J’ai ensuite proposé une technique non intrusive pour réduire sa consommation énergétique. Ensuite, j’ai étendu cette stratégie à un autre langage de programmation célèbre pour sa base de code ancienne, Java, pour montrer que nous pouvons encore réduire la consommation d’énergie d’applications déjà en cours d’exécution sans payer un prix considérable. Enfin, j’ai adopté une approche plus systémique. Au lieu d’optimiser une seule applica- tion, peut-on réduire la consommation d’énergie du centre de données dans son ensemble ? Grâce à l’architecture micro-services, une application peut être construite à l’aide de nom- breux services, tous indépendants les uns des autres. Ce type d’architecture nous libère de l’obligation d’adopter un seul langage de programmation comme le fait l’application monolithique. Et avec cela, on peu employer plusieurs langages de programmation et profiter des forces de chacun d’eux pour un scénario spécifique. Le dernier chapitre a analysé le com- portement énergétique de plusieurs langages de programmation concernant les services Web tout en ouvrant une nouvelle voie vers la durabilité au sein des applications intemporelles
Published: 2022

10. Green Coding : an Empirical Approach to Harness the Energy Consumption of Software Services

Author: belgaid, Mohammed chakib, Self-adaptation for distributed services and large software systems (SPIRALS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Lille University, Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189, SPIRALS - Self-adaptation for distributed services and large software systems, Romain Rouvoy, Lionel Seinturier, and belgaid, mohammed chakib
Subjects: Logiciels, [INFO.INFO-PL]Computer Science [cs]/Programming Languages [cs.PL], Économies d’énergie, Langages de programmation, [INFO.INFO-SE] Computer Science [cs]/Software Engineering [cs.SE], java, [INFO.INFO-SE]Computer Science [cs]/Software Engineering [cs.SE], [INFO] Computer Science [cs], langage de programmation, [INFO.INFO-PL] Computer Science [cs]/Programming Languages [cs.PL], Serveurs, green coding, python, servers, programming languages, energy consumption, energy measurement, datacenter, [INFO]Computer Science [cs], Centre de traitement informatique, Consommation d’énergie, Développement
Abstract: The ICT sector is claimed to account for 2% of global emissions. Even though this might seem like a small number, the success of ICT technologies will always lead to more greenhouse gas emissions. In 2019, the number of data centers worldwide was 1.5 million, which is expected to reach 2.5 million by 2025. In this situation, lowering the emissions from the ICT sector depends on reducing the amount of energy used by data centers. There are three main methods to achieve this goal: improving the hardware’s efficiency, lowering the cooling systems’ energy consumption, or decreasing the energy consumption of the servers themselves. This thesis focuses on the last approach, which I believe is the most affordable one, as it does not require any physical changes to data centers. My goal is to assist developers in making more eco-friendly software services by providing them with tools and guidelines to create software that runs on servers while consuming less energy. To do so, I decided to pursue an empirical approach consisting of three steps: test, measure, and optimize.The reason for such a decision is to follow the rapid pace of the software industry. In fact, the software industry has one of the fastest growth rates, which makes it challenging to keep up with the newest technologies. So, instead of just reporting my insights, I gave practitioners the means and protocols to allow them to test their hypotheses. I believe that some of the insights shared as part of this thesis might already have become obsolete when published.Due to the urgency of the climate change issue, I decided first to harness the most popular yet energy-hungry programming language, Python. Therefore, I started by analyzing Python’s code’s energy behavior during its most commonly used cases. Then, I provided a non-intrusive technique to reduce its energy consumption. After that, I extended this strategy to another programming language famous for its legacy code base, Java, to show that we can still reduce the energy consumption of already running applications without paying a considerable price.Finally, I adopted a more systemic approach. Instead of optimizing one single application, can one reduce the energy consumption of the data center as a whole entity? Thanks to the micro-services architecture, one application can be constructed using many services, each independent of the other. This type of architecture releases us from the bond of adopting a single programming language as the monolithic application does. And with this, one can use multiple programming languages and take advantage of the strengths of each one for a specific scenario. The last chapter analyzed the energy behavior of several programming languages regarding web services while opening a new path toward sustainability within timeless applications., Le secteur des TIC serait responsable de 2% des émissions mondiales. Même si ce chiffre peut paraître faible, le succès des technologies TIC entraînera toujours une augmentation des émissions de gaz à effet de serre. En 2019, le nombre de centres de données dans le monde était de 1,5 million, et devrait atteindre 2,5 millions d’ici 2025. Dans cette situation, la diminution des émissions du secteur des TIC dépend de la réduction de la consommation énergétique des centres de données. Il existe trois méthodes principales pour atteindre cet objectif : améliorer l’efficacité du matériel, faire baisser la consommation énergétique des systèmes de refroidissement, ou diminuer la consommation énergétique des serveurs eux- mêmes. Cette thèse se focalise sur la dernière approche, qui me semble être la plus abordable, car elle ne nécessite aucun changement physique dans les centres de données.Mon objectif est d’aider les développeurs à créer des logiciels plus écologiques en leur fournissant des outils et des directives pour créer des applications qui tournent sur des serveurs tout en consommant moins d’énergie. Pour ce faire, j’ai décidé d’adopter une approche empirique en trois étapes : tester, mesurer et optimiser.La raison d’une telle décision est de suivre le rythme rapide de l’industrie du logiciel. En fait, le secteur du logiciel connaît l’un des taux de croissance les plus rapides, ce qui rend difficile de suivre les nouvelles technologies. Ainsi, au lieu de me contenter de rapporter juste mes réflexions, j’ai fourni aux praticiens les moyens et les protocoles nécessaires pour leur permettre de tester leurs hypothèses. Je suis convaincu que certaines des conclusions partagées dans le cadre de cette thèse pourraient déjà être obsolètes au moment de leur publication.Vue l’urgence de la question du changement climatique, j’ai décidé d’abord d’exploiter le langage de programmation le plus populaire et pourtant le plus gourmand en énergie, Python. J’ai donc commencé par analyser le comportement énergétique du code Python dans ses utilisations les plus courantes. J’ai ensuite proposé une technique non intrusive pour réduire sa consommation énergétique. Ensuite, j’ai étendu cette stratégie à un autre langage de programmation célèbre pour sa base de code ancienne, Java, pour montrer que nous pouvons encore réduire la consommation d’énergie d’applications déjà en cours d’exécution sans payer un prix considérable. Enfin, j’ai adopté une approche plus systémique. Au lieu d’optimiser une seule applica- tion, peut-on réduire la consommation d’énergie du centre de données dans son ensemble ? Grâce à l’architecture micro-services, une application peut être construite à l’aide de nom- breux services, tous indépendants les uns des autres. Ce type d’architecture nous libère de l’obligation d’adopter un seul langage de programmation comme le fait l’application monolithique. Et avec cela, on peu employer plusieurs langages de programmation et profiter des forces de chacun d’eux pour un scénario spécifique. Le dernier chapitre a analysé le com- portement énergétique de plusieurs langages de programmation concernant les services Web tout en ouvrant une nouvelle voie vers la durabilité au sein des applications intemporelles
Published: 2022

11. Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty

Author: Biggs, Felix, Guedj, Benjamin, Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract: We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce the variance of its empirical counterpart, tightening the bound. We combine this with a new bound for $[-1, 1]$-valued (and potentially non-independent) signed losses, which is more favourable when they empirically have low variance around $0$. The primary new technical tool is a novel result for sequences of interdependent random vectors which may be of independent interest. We empirically evaluate these new bounds on a number of real-world datasets., 22 pages
Published: 2022

12. An extension of the angular synchronization problem to the heterogeneous setting

Author: Cucuringu, M, Tyagi, H, Department of Statistics [Oxford], University of Oxford [Oxford], MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, University of Oxford, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, group synchronization, Computer Science - Information Theory, Information Theory (cs.IT), singular value decomposition, Machine Learning (stat.ML), Numerical Analysis (math.NA), random matrix theory, Machine Learning (cs.LG), Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Mathematics - Numerical Analysis, spectral algorithms, matrix perturbation theory
Abstract: Given an undirected measurement graph $G = ([n], E)$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of the form $(\theta_i - \theta_j) \mod 2\pi$, for each $\{i,j\} \in E$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from preference relationships. In this paper, we consider a generalization to the setting where there exist $k$ unknown groups of angles $\theta_{l,1}, \dots,\theta_{l,n}$, for $l=1,\dots,k$. For each $ \{i,j\} \in E$, we are given noisy pairwise measurements of the form $\theta_{\ell,i} - \theta_{\ell,j}$ for an unknown $\ell \in \{1,2,\ldots,k\}$. This can be thought of as a natural extension of the angular synchronization problem to the heterogeneous setting of multiple groups of angles, where the measurement graph has an unknown edge-disjoint decomposition $G = G_1 \cup G_2 \ldots \cup G_k$, where the $G_i$'s denote the subgraphs of edges corresponding to each group. We propose a probabilistic generative model for this problem, along with a spectral algorithm for which we provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise. The theoretical findings are complemented by a comprehensive set of numerical experiments, showcasing the efficacy of our algorithm under various parameter regimes. Finally, we consider an application of bi-synchronization to the graph realization problem, and provide along the way an iterative graph disentangling procedure that uncovers the subgraphs $G_i$, $i=1,\ldots,k$ which is of independent interest, as it is shown to improve the final recovery accuracy across all the experiments considered., Comment: 45 pages, 17 figures
Published: 2022

13. Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates

Author: Michael Goldman, Benoît Merlet, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Michael Goldman is partially supported by the ANR SHAPO. Benoît Merlet is partially supported by the INRIA team RAPSODI and the Labex CEMPI (ANR-11-LABX-0007-01)., ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Paul Painlevé (LPP), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
Subjects: Physics, Smoothness (probability theory), Regular polygon, Mathematics::General Topology, Rigidity (psychology), Space (mathematics), Omega, Theoretical Computer Science, Combinatorics, Mathematics::Logic, Mathematics - Analysis of PDEs, Mathematics (miscellaneous), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Converse implication, Analysis of PDEs (math.AP)
Abstract: We study a family of non-convex functionals $\{\mathcal{E}\}$ on the space of measurable functions$u: \Omega_1\times\Omega_2 \subset \mathbb{R}^{n_1}\times\mathbb{R}^{n_2} \to \mathbb{R}$. These functionals vanish on the non-convex subset $S(\Omega_1\times\Omega_2)$ formed by functions of the form $u(x_1,x_2)=u_1(x_1)$ or $u(x_1,x_2)=u_2(x_2)$. We investigate under which conditions the converse implication "$\mathcal{E}(u) = 0 \Rightarrow u \in S(\Omega_1\times\Omega_2)$" holds. In particular, we show that the answer depends strongly on the smoothness of u. We also obtain quantitative versions of this implication by proving that (at least for some parameters) $\mathcal{E}(u)$ controls in a strong sense the distance of $u$ to $S(\Omega_1\times\Omega_2)$.
Published: 2021

14. Technical report: Object-centric Access Control Mechanisms in Dynamic Languages

Author: Rogliano, Théo, Polito, Guillermo, Tesone, Pablo, Fabresse, Luc, Ducasse, Stéphane, Analyses and Languages Constructs for Object-Oriented Application Evolution (RMOD), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Ecole nationale supérieure Mines-Télécom Lille Douai (IMT Nord Europe), Institut Mines-Télécom [Paris] (IMT), and Inria Lille Nord Europe - Laboratoire CRIStAL - Université de Lille
Subjects: [INFO.INFO-PL]Computer Science [cs]/Programming Languages [cs.PL]
Published: 2022

15. Technical Report: Unanticipated Object Synchronisation for Dynamically-Typed Languages

Author: Rogliano, Théo, Polito, Guillermo, Tesone, Pablo, Fabresse, Luc, Ducasse, Stéphane, Analyses and Languages Constructs for Object-Oriented Application Evolution (RMOD), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Ecole nationale supérieure Mines-Télécom Lille Douai (IMT Nord Europe), Institut Mines-Télécom [Paris] (IMT), and INRIA Lille - Nord Europe
Subjects: [INFO.INFO-PL]Computer Science [cs]/Programming Languages [cs.PL], Concurrency, Channels, Ownership, Dynamic Language, Permission Transfer
Abstract: Developing concurrent programs requires the use of threadsafe abstractions to avoid race conditions. Nevertheless, many libraries are not thread-safe either because it was not a concern for the developer or the developer purposely traded thread-safety for performance. All calls to such a library require to be synchronised in the client program. While different synchronisation mechanisms exist, only lock-based solutions and transaction solutions allow one to add synchronisation without anticipation. But they are both about reasoning in terms of execution. It forces developers to explore the whole execution to identify when synchronisation is required. A developer accidentally missing a synchronisation point circumvents the mechanism. Instead by ensuring exclusive access to an object for a thread prevents other thread to access it and thus allows developers to miss synchronisation points without circumventing the mechanism. In this paper, we propose the Atomic Samurai, a synchronisation model that is object-based, unanticipated, and while the object is synchronised the rest of the program normally runs concurrently. It relies on 3 mechanisms: pointer swapping to ensure reference unicity, proxies to control object accesses and late binding to intercept and redirect messages sent. We validate our approach by showing how Atomic Samurai helps both solving examples extracted from the literature and a real-world scenario from the Pharo community on font rendering. We also measure the impact in performance of our solution by comparing it with a semaphore-based solution. In term of performance, our solution is 5 orders of magnitude slower than the semaphore-based solution, but scales better with the number of processes.
Published: 2022

16. Entropy Regularized Reinforcement Learning with Cascading Networks

Author: Della Vecchia, Riccardo, Shilova, Alena, Preux, Philippe, Akrour, Riad, Scool (Scool), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Inria Lille Nord Europe - Laboratoire CRIStAL - Université de Lille
Subjects: Policy iteration, Cascade neural networks, mirror descent, réseaux de neurones en cascade, itération de politique, régularisation entropique, Entropy regularization, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: Deep Reinforcement Learning (Deep RL) has had incredible achievements on high dimensional problems, yet its learning process remains unstable even on the simplest tasks. Deep RL uses neural networks as function approximators. These neural models are largely inspired by developments in the (un)supervised machine learning community. Compared to these learning frameworks, one of the major difficulties of RL is the absence of i.i.d. data. One way to cope with this difficulty is to control the rate of change of the policy at every iteration. In this work, wechallenge the common practices of the (un)supervised learning community of using a fixed neural architecture, by having a neural model that grows in size at each policy update. This allows a closed form entropy regularized policy update, which leads to a better control of the rate of change of the policy at each iteration and help cope with the non i.i.d. nature of RL. Initial experiments on classical RL benchmarks show promising results with remarkable convergence on some RL tasks when compared to other deep RL baselines, while exhibiting limitations on others.; Ce travail étudie l’utilisation de réseaux de neurones en cascade qui permettent unemise à jour en forme close des politiques, dans le cadre d’algorithmes d’itération de politiqueavec régularisation entropique.
Published: 2022

17. Jumping Evaluation of Nested Regular Path Queries

Author: Azimov, Rustam, Niehren, Joachim, Salvati, Sylvain, Linking Dynamic Data (LINKS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Saint Petersburg State University (SPBU), The research was supported by the Russian Science Foundation grant 18-11-00100., Saint Petersburg State University [SPBU], Linking Dynamic Data [LINKS], Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189 (CRIStAL), Ecole Centrale de Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Ecole Centrale de Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: FOS: Computer and information sciences, Computer Science - Computational Complexity, Computer Science - Logic in Computer Science, [INFO.INFO-DB]Computer Science [cs]/Databases [cs.DB], Computer Science - Databases, Computer Science - Data Structures and Algorithms, InformationSystems_DATABASEMANAGEMENT, Databases (cs.DB), Data Structures and Algorithms (cs.DS), Computational Complexity (cs.CC), Logic in Computer Science (cs.LO)
Abstract: Nested regular path queries are used for querying graph databases and RDF triple stores. We propose a new algorithm for evaluating nested regular path queries on a graph from a set of start nodes in combined linear time. We show that this complexity upper bound can be reduced by making it dependent on the size of the query's top-down needed subgraph, a notion that we introduce. For many queries in practice, the top-down needed subgraph is way smaller than the whole graph. Our algorithm is based on a novel compilation schema from nested regular path queries to monadic datalog queries. Its complexity upper bound follows from known properties of top-down datalog evaluation. As an application, we show that our algorithm permits to reformulate in simple terms a variant of a very efficient automata-based algorithm proposed by Maneth and Nguyen that evaluates navigational path queries in datatrees based on indexes and jumping. Moreover, it overcomes some limitations of Maneth and Nguyen's: it is not bound to trees and applies to graphs; it is not limited to forward navigational XPath but can treat any nested regular path query and it can be implemented efficiently without any dedicated techniques, by using any efficient datalog evaluator such as LogicBlox., In Proceedings ICLP 2022, arXiv:2208.02685
Published: 2022

18. MMD Aggregated Two-Sample Test

Author: Schrab, Antonin, Kim, Ilmun, Albert, Mélisande, Laurent, Béatrice, Guedj, Benjamin, Gretton, Arthur, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), University College of London [London] (UCL), Yonsei University, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), Gatsby Computational Neuroscience Unit, Partial support from the French National Agency for Research, grants ANR-18-CE40-0016-01 and ANR-18-CE23-0015-02, ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Computer science department [University College London] (UCL-CS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, Kernel methods, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Minimax adaptivity, Machine Learning (cs.LG), Methodology (stat.ME), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Two-sample testing, FOS: Mathematics, Statistics - Methodology
Abstract: We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD). First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to determine the test threshold. We prove that this test controls the probability of type I error non-asymptotically. Hence, it can be used reliably even in settings with small sample sizes as it remains well-calibrated, which differs from previous MMD tests which only guarantee correct test level asymptotically. When the difference in densities lies in a Sobolev ball, we prove minimax optimality of our MMD test with a specific kernel depending on the smoothness parameter of the Sobolev ball. In practice, this parameter is unknown and, hence, the optimal MMD test with this particular kernel cannot be used. To overcome this issue, we construct an aggregated test, called MMDAgg, which is adaptive to the smoothness parameter. The test power is maximised over the collection of kernels used, without requiring held-out data for kernel selection (which results in a loss of test power), or arbitrary kernel choices such as the median heuristic. We prove that MMDAgg still controls the level non-asymptotically, and achieves the minimax rate over Sobolev balls, up to an iterated logarithmic term. Our guarantees are not restricted to a specific type of kernel, but hold for any product of one-dimensional translation invariant characteristic kernels. We provide a user-friendly parameter-free implementation of MMDAgg using an adaptive collection of bandwidths. We demonstrate that MMDAgg significantly outperforms alternative state-of-the-art MMD-based two-sample tests on synthetic data satisfying the Sobolev smoothness assumption, and that, on real-world image data, MMDAgg closely matches the power of tests leveraging the use of models such as neural networks., 80 pages
Published: 2022

19. Efficient Aggregated Kernel Tests using Incomplete $U$-statistics

Author: Antonin Schrab, Ilmun Kim, Benjamin Guedj, Arthur Gretton, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Guedj, Benjamin
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), Methodology (stat.ME), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics, Statistics - Methodology
Abstract: We propose a series of computationally efficient nonparametric tests for the two-sample, independence, and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC), and Kernel Stein Discrepancy (KSD), respectively. Our test statistics are incomplete $U$-statistics, with a computational cost that interpolates between linear time in the number of samples, and quadratic time, as associated with classical $U$-statistic tests. The three proposed tests aggregate over several kernel bandwidths to detect departures from the null on various scales: we call the resulting tests MMDAggInc, HSICAggInc and KSDAggInc. This procedure provides a solution to the fundamental kernel selection problem as we can aggregate a large number of kernels with several bandwidths without incurring a significant loss of test power. For the test thresholds, we derive a quantile bound for wild bootstrapped incomplete $U$-statistics, which is of independent interest. We derive non-asymptotic uniform separation rates for MMDAggInc and HSICAggInc, and quantify exactly the trade-off between computational efficiency and the attainable rates: this result is novel for tests based on incomplete $U$-statistics, to our knowledge. We further show that in the quadratic-time case, the wild bootstrap incurs no penalty to test power over the more widespread permutation-based approach, since both attain the same minimax optimal rates (which in turn match the rates that use oracle quantiles). We support our claims with numerical experiments on the trade-off between computational efficiency and test power. In all three testing frameworks, the linear-time versions of our proposed tests perform at least as well as the current linear-time state-of-the-art tests., 34 pages, 5 figures
Published: 2022

20. On Margins and Generalisation for Voting Classifiers

Author: Biggs, Felix, Zantedeschi, Valentina, Guedj, Benjamin, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Guedj, Benjamin
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Mathematics - Statistics Theory, Machine Learning (stat.ML), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), ComputingMethodologies_PATTERNRECOGNITION, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics
Abstract: We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. [2021] for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the "margins theory" proposed by Schapire et al. [1998] for the generalisation of ensemble classifiers., Comment: 20 pages, 8 figures
Published: 2022

21. Project-Team RMOD 2021 Activity Report

Author: Denker, Marcus, Anquetil, Nicolas, Aranega, Vincent, Costiou, Steven, Ducasse, Stéphane, Etien, Anne, Analyses and Languages Constructs for Object-Oriented Application Evolution (RMOD), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and INRIA Lille - Nord Europe
Subjects: [INFO.INFO-PL]Computer Science [cs]/Programming Languages [cs.PL]
Published: 2022

22. Stefan problem for a nonergodic facilitated exclusion process

Author: Clément Erignoux, Oriane Blondel, Marielle Simon, Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Paradyse, Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Clément Erignoux gratefully acknowledges funding from the European Research Council (ERC) under the European Unions Horizon 2020 Program, ERC Consolidator Grant UniCoSM (grant agreement no724939). Marielle Simon thanks Labex CEMPI (ANR-11-LABX-0007-01). Oriane Blondel thanks the ANR projects LSD (ANR-15-CE40-0020) and MALIN (ANR-16-CE93-0003) and acknowledges support from INSMI (CNRS) through a PEPS JCJC grant. This project is partially supported by the ANR grant MICMOV (ANR-19-CE40-0012) of the French National Research Agency (ANR), and it has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative program (grant agreement n° 715734)., ANR-19-CE40-0012,MICMOV,Description microscopique des interfaces mobiles(2019), ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2016), ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), European Project: 715734,H2020,HyLEF(2016), European Project: 724939,UniCoSM, Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Università degli Studi Roma Tre, Méthodes quantitatives pour les modèles aléatoires de la physique (MEPHYSTO-POST), Inria Lille - Nord Europe, ANR-19-CE40-0012,MICMOV,Microscopic Description of Moving Interfaces(2020), ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2017), ANR-15-CE40-0020,LSD,Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics(2015), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Systèmes de particules et systèmes dynamiques (Paradyse), Laboratoire Paul Painlevé (LPP), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
Subjects: Physics, Probability (math.PR), 010102 general mathematics, Degenerate energy levels, Lattice (group), Stefan problem, 01 natural sciences, 010305 fluids & plasmas, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], kinetically constrained exclusion process, active-absorbing phase transition, 0103 physical sciences, FOS: Mathematics, Jump, Free boundary problem, Hydrodynamic limits, Ergodic theory, Limit (mathematics), Statistical physics, 0101 mathematics, Mathematics - Probability, Irreducible component
Abstract: International audience; We consider the facilitated exclusion process, which is a non-ergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve on the one-dimensional lattice according to jump rates which are degenerate, since they can vanish on non-trivial configurations and create distinct phases: indeed, configurations can be totally blocked (they cannot evolve under the dynamics), ergodic (they belong to an irreducible component), or transient (after a transitive period of time they will become either blocked or ergodic). We additionally prove that the microscopic separation into blocked/ergodic phases fully coincides with the moving interface problem given by the hydrodynamic equation.
Published: 2021

23. Linear Programs with Conjunctive Queries

Author: Capelli, Florent, Crosetti, Nicolas, Niehren, Joachim, Ramon, Jan, Linking Dynamic Data (LINKS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Machine Learning in Information Networks (MAGNET), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: hypergraph decomposition, [INFO.INFO-DB]Computer Science [cs]/Databases [cs.DB], linear programming, Theory of computation �� Logic and databases, Database queries
Abstract: In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The naive approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s-measure of patterns in graphs as needed for data mining., LIPIcs, Vol. 220, 25th International Conference on Database Theory (ICDT 2022), pages 5:1-5:19
Published: 2022

24. Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method

Author: Karlé, Eglantine, Tyagi, Hemant, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Laboratoire Paul Painlevé - UMR 8524 (LPP), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe
Subjects: FOS: Computer and information sciences, [STAT]Statistics [stat], Statistics - Machine Learning, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [MATH]Mathematics [math]
Abstract: Many applications such as recommendation systems or sports tournaments involve pairwise comparisons within a collection of $n$ items, the goal being to aggregate the binary outcomes of the comparisons in order to recover the latent strength and/or global ranking of the items. In recent years, this problem has received significant interest from a theoretical perspective with a number of methods being proposed, along with associated statistical guarantees under the assumption of a suitable generative model. While these results typically collect the pairwise comparisons as one comparison graph $G$, however in many applications - such as the outcomes of soccer matches during a tournament - the nature of pairwise outcomes can evolve with time. Theoretical results for such a dynamic setting are relatively limited compared to the aforementioned static setting. We study in this paper an extension of the classic BTL (Bradley-Terry-Luce) model for the static setting to our dynamic setup under the assumption that the probabilities of the pairwise outcomes evolve smoothly over the time domain $[0,1]$. Given a sequence of comparison graphs $(G_{t'})_{t' \in \mathcal{T}}$ on a regular grid $\mathcal{T} \subset [0,1]$, we aim at recovering the latent strengths of the items $w_t^* \in \mathbb{R}^n$ at any time $t \in [0,1]$. To this end, we adapt the Rank Centrality method - a popular spectral approach for ranking in the static case - by locally averaging the available data on a suitable neighborhood of $t$. When $(G_{t'})_{t' \in \mathcal{T}}$ is a sequence of Erd\"os-Renyi graphs, we provide non-asymptotic $\ell_2$ and $\ell_{\infty}$ error bounds for estimating $w_t^*$ which in particular establishes the consistency of this method in terms of $n$, and the grid size $\lvert\mathcal{T}\rvert$. We also complement our theoretical analysis with experiments on real and synthetic data., Comment: 52 pages, 5 figures, 4 tables, revised as per reviewer comments, added section 3.3 and additional experiment results
Published: 2022

25. Stochastic modulational instability in the nonlinear Schr\'odinger equation with colored random dispersion

Author: Andrea Armaroli, Guillaume Dujardin, Alexandre Kudlinski, Arnaud Mussot, Stefano Trillo, Stephan De Bièvre, Matteo Conforti, Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Systèmes de particules et systèmes dynamiques (Paradyse), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Università degli Studi di Ferrara = University of Ferrara (UniFE), ANR-16-IDEX-0004,ULNE,ULNE(2016), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Paradyse, Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, and Università degli Studi di Ferrara (UniFE)
Subjects: optical fibers, nonlinear optics, FOS: Physical sciences, frequency conversion, Pattern Formation and Solitons (nlin.PS), disorder, 01 natural sciences, Nonlinear Sciences - Pattern Formation and Solitons, NO, optical fibers, frequency conversion, nonlinear optics, disorder, 010309 optics, [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], 0103 physical sciences, [SPI.OPTI]Engineering Sciences [physics]/Optics / Photonic, 010306 general physics, Optics (physics.optics), Physics - Optics
Abstract: We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wavenumber, we obtain low-frequency MI sidelobes which converge to those given by a white noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD, 12 pages, 6 figures submitted
Published: 2022

26. Long-time behavior of SSEP with slow boundary

Author: Linjie Zhao, Paradyse, Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-19-CE40-0012,MICMOV,Description microscopique des interfaces mobiles(2019), Systèmes de particules et systèmes dynamiques (Paradyse), Laboratoire Paul Painlevé (LPP), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
Subjects: Statistics and Probability, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], slow boundary, Probability (math.PR), Exclusion process, FOS: Mathematics, law of large numbers, empirical measure, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract: We consider the symmetric simple exclusion process with slow boundary first introduced in [Baldasso {\it et al.}, Journal of Statistical Physics, 167(5), 2017]. We prove a law of large number for the empirical measure of the process under a longer time scaling instead of the usual diffusive time scaling., 12 pages
Published: 2022

27. Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods

Author: Chaumont-Frelet, Théophile, Ern, Alexandre, Lemaire, Simon, Valentin, Frédéric, Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Laboratorio Nacional de Computação Cientifica [Rio de Janeiro] (LNCC / MCT), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Laboratoire Jean Alexandre Dieudonné (LJAD), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)
Subjects: Numerical Analysis (math.NA), 010103 numerical & computational mathematics, 01 natural sciences, Highly heterogeneous diffusion, 010101 applied mathematics, High-order methods, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General polytopal meshes, Mathematics - Numerical Analysis, 0101 mathematics, Multiscale methods, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. We also leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.
Published: 2022

28. An end-to-end data-driven optimisation framework for constrained trajectories

Author: Florent Dewez, Benjamin Guedj, Arthur Talpaert, Vincent Vandewalle, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, Université de Lille, Laboratoire Paul Painlevé - UMR 8524 (LPP), and Computer science department [University College London] (UCL-CS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.AP]Statistics [stat]/Applications [stat.AP], Constrained optimisation Contents, Machine Learning (stat.ML), Statistics - Applications, Functional data, Machine Learning (cs.LG), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Applications (stat.AP), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Statistical modelling, Mathematics - Optimization and Control
Abstract: Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of reach. In this paper, we leverage data-driven approaches to design a new end-to-end framework which is dynamics-free for optimised and realistic trajectories. We first decompose the trajectories on function basis, trading the initial infinite dimension problem on a multivariate functional space for a parameter optimisation problem. A maximum \emph{a posteriori} approach which incorporates information from data is used to obtain a new optimisation problem which is regularised. The penalised term focuses the search on a region centered on data and includes estimated linear constraints in the problem. We apply our data-driven approach to two settings in aeronautics and sailing routes optimisation, yielding commanding results. The developed approach has been implemented in the Python library PyRotor., Comment: 28 pages
Published: 2022

29. On Deterministic Numerical Methods for the quantum Boltzmann-Nordheim Equation. I. Spectrally accurate approximations, Bose-Einstein condensation, Fermi-Dirac saturation

Author: Alexandre Mouton, Thomas Rey, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Reliable numerical approximations of dissipative systems (RAPSODI ), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-17-CE40-0027,MoHyCon,Modèles multi-échelles et simulation numérique hybride de semi-conducteurs(2017), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe
Subjects: Condensed Matter::Quantum Gases, Numerical Analysis, 050208 finance, Boltzmann-Nordheim equation, Physics and Astronomy (miscellaneous), Applied Mathematics, 05 social sciences, spectral method, 76P05, 65N35, 82C40, Numerical Analysis (math.NA), Fermi-Dirac saturation, Bose-Einstein condensation, large time behavior, Computer Science Applications, Computational Mathematics, quantum, Modeling and Simulation, 0502 economics and business, FOS: Mathematics, Mathematics - Numerical Analysis, 050207 economics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This equation, modeled on the seminal Boltzmann equation, describes using a statistical physics formalism the time evolution of a gas composed of bosons or fermions. Using the spectral-Galerkin algorithm introduced in [F. Filbet, J. Hu, and S. Jin, ESAIM: Math. Model. Numer. Anal., 2011], together with some novel parallelization techniques, we investigate some of the conjectured properties of the large time behavior of the solutions to this equation. In particular, we are able to observe numerically both Bose-Einstein condensation and Fermi-Dirac relaxation.
Published: 2022

30. Regular Matching and Inclusion on Compressed Tree Patterns with Constrained Context Variables

Author: Iovka Boneva, Joachim Niehren, Momar Sakho, Linking Dynamic Data (LINKS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), This work was partially supported by a grant from CPER Nord-Pas de Calais/FEDER DATA Advanced data science and technologies 2015-2020., Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC], Matching (statistics), Theoretical computer science, Computational complexity theory, tree patterns, computer.internet_protocol, Computer science, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, tree automata, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Theoretical Computer Science, [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL], 0202 electrical engineering, electronic engineering, information engineering, Time complexity, Computer Science::Databases, computational complexity, Context variable, Xml, Hedge (linguistics), streams, Computer Science Applications, Tree (data structure), Computational Theory and Mathematics, 010201 computation theory & mathematics, 020201 artificial intelligence & image processing, Inclusion (education), computer, XML, grammar compression, Information Systems
Abstract: International audience; We study the complexity of regular matching and inclusion for compressed tree patterns with context variables subject to regular constraints. Context variables with regular constraints permit to properly generalize on unranked tree patterns with hedge variables. Regular inclusion on unranked tree patterns is relevant to certain query answering on Xml streams with references. We show that regular matching and inclusion with regular constraints can be reduced in polynomial time to the corresponding problem without regular constraints.
Published: 2022

31. Strategic bidding in price coupled regions

Author: Jérôme De Boeck, Luce Brotcorne, Bernard Fortz, Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Graphes et Optimisation Mathématique [Bruxelles] (GOM), Université libre de Bruxelles (ULB), This research benefited from the support of the FMJH Program PGMO and from the support of EDF,Thales, Orange., Université libre de Bruxelles (ULB)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)
Subjects: 021103 operations research, 020209 energy, General Mathematics, Bilevel optimization, MILP reformulation, 0211 other engineering and technologies, 02 engineering and technology, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], Management Science and Operations Research, Extended formulations, 0202 electrical engineering, electronic engineering, information engineering, Strategic bidding, MPEC, Software
Abstract: International audience; With the emerging deregulated electricity markets, a part of the electricity trading takes place in dayahead markets where producers and retailers place bids in order to maximize their profit. We present a price-maker model for strategic bidding from the perspective of a producer in Price Coupled Regions (PCR) considering a capacitated transmission network between local day-ahead markets. The aim for the bidder is to establish a production plan and set its bids taking into consideration the reaction of the market. We consider the problem as deterministic, that is, the bids of the competitors are known in advance. We are facing a bilevel optimization problem where the first level is a Unit Commitment problem, modeled as a Mixed Integer Linear Program (MILP), and the second level models a market equilibrium problem through a Linear Program. The problem is first reformulated as a single level problem. Properties of the optimal spot prices are studied to obtain an extended formulation that is linearized and tightened using new valid inequalities. Several properties of the spot prices allow to reduce significantly the number of binary variables. Two novel heuristics are proposed, the first applicable in PCR, the second for general formulations with Special Ordered Sets (SOS) of type 1. Our computational experiments highlights the risk of a loss for the bidder if some aspects usually not considered in the literature, such as Price Coupled Regions, or an accurate UC problem, are not taken into account. They also show that the reformulation techniques, combined with new valid inequalities, allow to solve much larger instances than the current state-of-the-art. Finally, our experiments also show that the proposed heuristics deliver very high quality solutions in a short computation time.
Published: 2022

32. Model-based Clustering with Missing Not At Random Data

Author: Sportisse, Aude, Biernacki, Christophe, Boyer, Claire, Josse, Julie, Marbac Lourdelle, Matthieu, Celeux, Gilles, Laporte, Fabien, Université Côte d'Azur (UCA), Modèles et algorithmes pour l’intelligence artificielle (MAASAI), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UNIV-RENNES), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI), Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Economie et Statistique [Bruz] (CREST), Université Lille Nord (France), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Sorbonne Université (SU), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Desbrest de santé publique (IDESP), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Médecine de précision par intégration de données et inférence causale (PREMEDICAL), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Desbrest de santé publique (IDESP), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Nantes Université (Nantes Univ), Institut du Thorax [Nantes], INSERM U649, Nantes, Institut National de la Santé et de la Recherche Médicale (INSERM), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), ANR-16-IDEX-0006,MUSE,MUSE(2016), Inria Lille - Nord Europe, Université Catholique de l'Ouest (UCO), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université de Rennes (UR), Laboratoire Paul Painlevé (LPP), Statistique mathématique et apprentissage (CELESTE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Missing Not At Random (MNAR) Data, Model-based Clustering, Machine Learning (stat.ML), Identifiability, EM and Stochastic EM Algorithms, Machine Learning (cs.LG), Medical Data
Abstract: In recent decades, technological advances have made it possible to collect large data sets. In this context, the model-based clustering is a very popular, flexible and interpretable methodology for data exploration in a well-defined statistical framework. One of the ironies of the increase of large datasets is that missing values are more frequent. However, traditional ways (as discarding observations with missing values or imputation methods) are not designed for the clustering purpose. In addition, they rarely apply to the general case, though frequent in practice, of Missing Not At Random (MNAR) values, i.e. when the missingness depends on the unobserved data values and possibly on the observed data values. The goal of this paper is to propose a novel approach by embedding MNAR data directly within model-based clustering algorithms. We introduce a selection model for the joint distribution of data and missing-data indicator. It corresponds to a mixture model for the data distribution and a general MNAR model for the missing-data mechanism, which may depend on the underlying classes (unknown) and/or the values of the missing variables themselves. A large set of meaningful MNAR sub-models is derived and the identifiability of the parameters is studied for each of the sub-models, which is usually a key issue for any MNAR proposals. The EM and Stochastic EM algorithms are considered for estimation. Finally, we perform empirical evaluations for the proposed submodels on synthetic data and we illustrate the relevance of our method on a medical register, the TraumaBase ® dataset.
Published: 2022

33. Cluster-Specific Predictions with Multi-Task Gaussian Processes

Author: Leroy, Arthur, Latouche, Pierre, Guedj, Benjamin, Gey, Servane, University of Manchester [Manchester], Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Engineering and Physical Sciences Research Council (EPSRC), grant number EP/R013616/1, ANR-18-CE40-0016,BEAGLE,Apprentissage PAC-bayésien agnostique(2018), ANR-18-CE23-0015,APRIORI,Une Perspective PAC-Bayésienne de l'Apprentissage de Représentations(2018), Computer science department [University College London] (UCL-CS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC)
Subjects: FOS: Computer and information sciences, cluster-specific predictions, Computer Science - Machine Learning, Gaussian processes mixture, multi-task learning, Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], curve clustering, Statistics - Computation, variational EM, Machine Learning (cs.LG), Methodology (stat.ME), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [STAT.CO]Statistics [stat]/Computation [stat.CO], Computation (stat.CO), Statistics - Methodology
Abstract: A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package., 47 pages
Published: 2022

34. Reprint: a randomized extrapolation based on principal components for data augmentation

Author: Wei, Jiale, Chen, Qiyuan, Peng, Pai, Guedj, Benjamin, Li, Le, Guedj, Benjamin, Central China Normal University [Wuhan, China], University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), National Natural Science Foundation of China (Grant No. 62107021), and Hubei ProvincialScience and Technology Innovation Base (Platform) Special Project 2020DFH002
Subjects: FOS: Computer and information sciences, History, Computer Science - Computation and Language, Principal components, Polymers and Plastics, Data augmentation, Hidden-space representation, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Randomised extrapolation, Industrial and Manufacturing Engineering, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-CL] Computer Science [cs]/Computation and Language [cs.CL], Business and International Management, Computation and Language (cs.CL)
Abstract: Data scarcity and data imbalance have attracted a lot of attention in many fields. Data augmentation, explored as an effective approach to tackle them, can improve the robustness and efficiency of classification models by generating new samples. This paper presents REPRINT, a simple and effective hidden-space data augmentation method for imbalanced data classification. Given hidden-space representations of samples in each class, REPRINT extrapolates, in a randomized fashion, augmented examples for target class by using subspaces spanned by principal components to summarize distribution structure of both source and target class. Consequently, the examples generated would diversify the target while maintaining the original geometry of target distribution. Besides, this method involves a label refinement component which allows to synthesize new soft labels for augmented examples. Compared with different NLP data augmentation approaches under a range of data imbalanced scenarios on four text classification benchmark, REPRINT shows prominent improvements. Moreover, through comprehensive ablation studies, we show that label refinement is better than label-preserving for augmented examples, and that our method suggests stable and consistent improvements in terms of suitable choices of principal components. Moreover, REPRINT is appealing for its easy-to-use since it contains only one hyperparameter determining the dimension of subspace and requires low computational resource.
Published: 2022
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35. Online PAC-Bayes Learning

Author: Haddouche, Maxime, Guedj, Benjamin, Guedj, Benjamin, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science::Machine Learning, Computer Science - Machine Learning, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], TheoryofComputation_GENERAL, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics
Abstract: Most PAC-Bayesian bounds hold in the batch learning setting where data is collected at once, prior to inference or prediction. This somewhat departs from many contemporary learning problems where data streams are collected and the algorithms must dynamically adjust. We prove new PAC-Bayesian bounds in this online learning framework, leveraging an updated definition of regret, and we revisit classical PAC-Bayesian results with a batch-to-online conversion, extending their remit to the case of dependent data. Our results hold for bounded losses, potentially \emph{non-convex}, paving the way to promising developments in online learning., 21 pages
Published: 2022

36. On the local and global properties of gravitational spheres of influence

Author: F Pierret, D Souami, Jacky Cresson, Christophe Biernacki, Laboratoire d'études spatiales et d'instrumentation en astrophysique = Laboratory of Space Studies and Instrumentation in Astrophysics (LESIA), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'études spatiales et d'instrumentation en astrophysique (LESIA (UMR_8109)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies
Subjects: 010504 meteorology & atmospheric sciences, FOS: Physical sciences, Motion (geometry), Context (language use), 01 natural sciences, Gravitation, Planet, Celestial mechanics, 0103 physical sciences, 010303 astronomy & astrophysics, Solar and Stellar Astrophysics (astro-ph.SR), 0105 earth and related environmental sciences, [PHYS]Physics [physics], Earth and Planetary Astrophysics (astro-ph.EP), Physics, [SDU.ASTR.SR]Sciences of the Universe [physics]/Astrophysics [astro-ph]/Solar and Stellar Astrophysics [astro-ph.SR], Equations of motion, Astronomy and Astrophysics, Planetary system, Planetary systems, Classical mechanics, Astrophysics - Solar and Stellar Astrophysics, Space and Planetary Science, Hill sphere, Astrophysics::Earth and Planetary Astrophysics, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], [STAT.ME]Statistics [stat]/Methodology [stat.ME], Astrophysics - Earth and Planetary Astrophysics
Abstract: We revisit the concept of sphere of gravitational activity, to which we give both a geometrical and physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc-Star-Planets system) to define a first order "border" of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the 3-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of planet's sphere of activity as the region of space in which it is feasible to assume a planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite's motion. We then investigate the geometrical properties and physical meaning of the ratios of Solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. We clearly distinguish throughout the paper between the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, taking a closer look and comparing the ratio of the star's accelerations (central/perturbing) to that of the planetary acceleration (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes which are presented in the semi-analytical analysis., Comment: 11 pages, 5 figures
Published: 2020

37. Traveling waves for some nonlocal 1D Gross–Pitaevskii equations with nonzero conditions at infinity

Author: André de Laire, Pierre Mennuni, Méthodes quantitatives pour les modèles aléatoires de la physique (MEPHYSTO-POST), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Systèmes de particules et systèmes dynamiques (Paradyse), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, The authors acknowledge support from the Labex CEMPI (ANR-11-LABX0007-01). A. de Laire was also supported by the ANR project ODA (ANR-18-CE40-0020-01)., ANR-18-CE40-0020,ODA,Ondes déterministes et aléatoires(2018), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Laboratoire Paul Painlevé - UMR 8524 (LPP), ANR-18-CE40-0020,ODA,RANDOM AND DETERMINISTIC WAVES(2018), ANR: 11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), and Paradyse
Subjects: dark solitons, orbital stability, media_common.quotation_subject, Dirac delta function, 010103 numerical & computational mathematics, 01 natural sciences, Momentum, symbols.namesake, Mathematics - Analysis of PDEs, Dimension (vector space), dark soli- tons, Simple (abstract algebra), Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Initial value problem, 0101 mathematics, media_common, Physics, Applied Mathematics, Mathematical analysis, 16. Peace & justice, Infinity, Nonlocal Schrödinger equation, 010101 applied mathematics, traveling waves, Gross–Pitaevskii equation, Mathematics - Classical Analysis and ODEs, symbols, Minification, 35Q55, 35J20, 35A15, 35C07, 35B35, 37K05, 35C08, 35Q53, 82D50, nonzero conditions at infinity, Gross-Pitaevskii equation, Analysis, Analysis of PDEs (math.AP)
Abstract: We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions with nonvanishing conditions at infinity. Moreover, we show that the branch is orbitally stable. In this manner, this result generalizes known properties for the contact interaction given by a Dirac delta function. Our proof relies on the minimization of the energy at fixed momentum. As a by-product of our analysis, we provide a simple condition to ensure that the solution to the Cauchy problem is global in time., 48 pages, 11 figures
Published: 2020

38. Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker–Planck equations

Author: Guillaume Dujardin, Pauline Lafitte, Frédéric Hérau, Systèmes de particules et systèmes dynamiques (Paradyse), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques Jean Leray (LMJL), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec-Université Paris-Saclay, Fédération de Mathématiques de CentraleSupélec (FR3487), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Guillaume Dujardin is supported by the Inria project-team MEPHYSTO and the Labex CEMPI (ANR-11-LABX-0007-01). Frédéric Hérau is supported by the grant 'NOSEVOL' ANR-2011-BS01-0019-01., ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-11-BS01-0019,NOSEVOL,Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution(2011), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Paradyse, Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), and Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487)
Subjects: Discretization, Applied Mathematics, Numerical analysis, Numerical Analysis (math.NA), 010103 numerical & computational mathematics, Derivative, Coercivity, Space (mathematics), 01 natural sciences, Exponential function, 010101 applied mathematics, Computational Mathematics, symbols.namesake, Poincaré conjecture, FOS: Mathematics, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, Fokker–Planck equation, Mathematics - Numerical Analysis, 0101 mathematics, Mathematics
Abstract: International audience; In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these dis-cretizations of velocity and space, we prove the exponential convergence to the equilibrium of the solutions, for time-continuous equations as well as for time-discrete equations. Our method uses new types of discrete Poincaré inequalities for a " two-direction " discretization of the derivative in velocity. For the inhomogeneous problem, we adapt hypocoercive methods to the discrete cases.
Published: 2019

39. Circulating proteomic signature of early death in heart failure patients with reduced ejection fraction

Author: Vincent Vandewalle, Audrey Hulot, Guillemette Marot, Christophe Bauters, Florence Pinet, Pascal de Groote, Maxime Brunin, Olivia Beseme, Marie Cuvelliez, Philippe Amouyel, Facteurs de Risque et Déterminants Moléculaires des Maladies liées au Vieillissement - U 1167 (RID-AGE), Institut Pasteur de Lille, Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Remodeling in Valvulopathy and Heart Failure [CHU Rouen] (FHU REMOD-VHF ), CHU Rouen, Normandie Université (NU)-Normandie Université (NU), MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, BILILLE, This work was supported by grants from the French Clinical Research Infrastructure Network INI-CRCT (Investigation Network Initiative-Cardiovascular and Renal Clinical Trialists), the E.U. FP7 HOMAGE (305507), 'Agence Nationale de Recherche' 15-CEA-U16/'Direction Générale de l’Offre de Soins' (5–013) and CHRU de Lille (Bonus H2018). We acknowledge Somalogic Inc. as the provider of the proteomics analysis and EdgeLeap B.V. for the systems biology analysis., Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut Pasteur de Lille, Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP), Laboratoire Paul Painlevé - UMR 8524 (LPP), Pinet, Florence, Evaluation des technologies de santé et des pratiques médicales - ULR 2694 [METRICS], Facteurs de Risque et Déterminants Moléculaires des Maladies liées au Vieillissement - U 1167 [RID-AGE], METRICS : Evaluation des technologies de santé et des pratiques médicales - ULR 2694, and Facteurs de risque et déterminants moléculaires des maladies liées au vieillissement (RID-AGE) - U1167
Subjects: Oncology, Male, Proteomics, medicine.medical_specialty, Proteome, [SDV]Life Sciences [q-bio], lcsh:Medicine, Context (language use), Cardiovascular System, Article, Gene regulatory networks, Prognostic markers, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Risk Factors, Internal medicine, Cause of Death, Medicine, Humans, lcsh:Science, Cathepsin S, Heart Failure, Ejection fraction, business.industry, lcsh:R, Middle Aged, medicine.disease, Blood proteins, [SDV.MHEP.CSC] Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, 3. Good health, Extracellular Matrix, [SDV] Life Sciences [q-bio], Clinical research, Heart failure, Biomarker (medicine), Female, lcsh:Q, business, Extracellular matrix organization
Abstract: Background: Heart failure (HF) remains a main cause of mortality worldwide. Risk stratification of patients with systolic chronic HF is critical to identify those who may benefit from advanced HF therapies. The aim of this study is to identify plasmatic proteins that could predict early death of HF patients. Methods: The subproteome targeted by the aptamer-based assay (SOMAscan) of 1310 proteins was profiled in blood samples from 168 HF patients with reduced ejection fraction hospitalized in CHRU de Lille. Patient's outcome was assessed 3 years after inclusion. Findings: Among the 1310 proteins, 203 were significantly modulated between dead and alive patients (Wilcoxon tests, FDR 5%). The INCA molecular network was built using these 203 proteins and contained 2881 molecules (1639 proteins, 1072 microRNAs, 170 metabolites). To assess mechanistic context of HF, molecules were assigned to 34 clusters annotated to biological pathways from Gene Ontology. Analysis of the INCA network model allowed to highlight extracellular matrix organization as mechanism involved in HF. In parallel, an adaptive LASSO was performed on these 203 proteins and six proteins were selected as candidates to predict early death of HF patients: complement C3, cathepsin S and FAM107B were decreased and MAPKAPK5, MMP1 and MMP7 increased in dead patients compared with patients alive. By conventional assays, complement C3, MMP1 and MMP7 were validated but not cathepsin S due to the low sensitivity and specificity of the assay used. Interpretation: A proteomic signature of 6 plasma proteins allows identifying HF patients with a risk of early death. Funding Statement: This work was supported by grants from French Clinical Research Infrastructure Network INI-CRT (Investigation Network Initiative-Cardiovascular and Renal Clinical Trialists), the E.U. FP7 HOMAGE (305507), “Agence Nationale de Recherche” 15-CEA-U16/”Direction Generale de l'Offre de Soins” (5- 013) and CHRU de Lille (Bonus H2018).We acknowledged Somalogic Inc as the provider of the proteomics analysis and EdgeLeap B.V. for the system biology analysis. Declaration of Interests: MC, VV, MB, OB, AH, PDG, PA, CB, GM, FP have no conflict of interest to disclose for the study performed. Ethics Approval Statement: The INCA study was approved by the ethics committee of the “Centre Hospitalier de Lille” (CP98/94, 5 November 1998) , and written informed consent was obtained for each patient.
Published: 2019

40. Towards more robust and accurate computations of capillary effects in the simulation of multiphase flows in porous media

Author: Bassetto, Sabrina, IFP Energies nouvelles (IFPEN), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Lille, Clément Cancès, Laboratoire Paul Painlevé (LPP), and Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe
Subjects: paramétrage, conditions d'interface, écoulement diphasique en milieu poreux, parametrization, Richards equation, méthode de Newton, Écoulement en milieu poreux, Saturation, two-phase flow in porous media, Flow in porous media, interface conditions, Pression capillaire, Newton's method, Capillary pressure, Équation de Richards, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Carbon dioxide capture, utilization and storage (CCUS) is a powerful technology to reduce the quantity of greenhouse gases emitted into the atmosphere. Generally, [dollar]ext{CO}_2[dollar] is stored in geological underground structures such as depleted oil and gas reservoirs or saline aquifer. Once injected into formations, [dollar]ext{CO}_2[dollar] is trapped underground by means of various trapping mechanisms. The formation heterogeneities and changes in wettability are involved in one of them. The discontinuities thus created are at the basis of the capillary barrier phenomenon, which plays a crucial role for flows in porous media and in fractured ones in particular.For Darcy flows, capillary pressure is often modeled as a function of fluid saturation and rock type. Each lithology corresponds to a capillary pressure-saturation curve which displays strong variations embodied by asymptotes. The change of curve induced by the change of rock requires to define precisely the interface conditions between two different lithologies in order to model the flow or the trapping of the fluids accurately through this interface. In view of these characteristics and constraints, numerical difficulties may arise when simulating these flows, especially during Newton iterations. Some choices of primary variables may be more appropriate than others.In this thesis, we aim at improving Newton robustness in order to overcome the above-mentioned difficulties and at proposing strategies to enforce transmission conditions at interfaces in heterogeneous domains. Our work follows an order of increasing difficulties. First, we start considering the easier model, the Richards equation, in a homogeneous medium. Then, we introduce heterogeneities in the domain. Finally, we turn to the complete model in a challenging configuration: the immiscible incompressible two-phase system in a heterogeneous domain.To improve robustness, we propose a strategy based on variable switch and it is easily implemented thanks to a fictitious variable that enables us to describe both the saturation and the pressure and that we call parametrization technique. The numerical tests performed confirm the potentiality of this technique, which allows the Richards equation to be solved without caring about the choice of the primary unknown and without any convergence problems.In a heterogeneous domain, a naive scheme without explicit inclusion of heterogeneities suffers from a lack of accuracy in the predicted results. This motivates the introduction of a specific treatment of the interfaces. Thus, we propose and compare several approaches to deal with the interface transmission condition, analyzing their pros and cons when confronted to different physical settings for the Richards equation as well as the two-phase Darcy flow model.; La séquestration du dioxyde de carbone (CCUS) constitue une technique puissante pour réduire la quantité de gaz à effet de serre émis dans l'atmosphère. En général, le CO2 est stocké dans des structures géologiques souterraines telles que des réservoirs de pétrole et de gaz épuisés ou des aquifères salins. Une fois injecté dans les formations, le CO2 est piégé en sous-sol au moyen de divers mécanismes de piégeage. Les hétérogénéités de la formation et les changements de mouillabilité interviennent dans l'un d'entre eux. Les discontinuités ainsi créées sont à la base du phénomène de barrière capillaire, qui joue un rôle crucial pour les écoulements en milieu poreux et en particulier dans les milieux fracturés.Pour les écoulements de Darcy, la pression capillaire est souvent modélisée comme une fonction de la saturation du fluide et du type de roche. Chaque lithologie correspond à une courbe de pression capillaire-saturation qui présente de fortes variations matérialisées par des asymptotes. Le changement de courbe induit par le changement de roche nécessite de définir précisément les conditions d'interface entre deux lithologies différentes afin de modéliser précisément l'écoulement ou le piégeage des fluides à travers cette interface. Compte tenu de ces caractéristiques et contraintes, des difficultés numériques peuvent apparaître lors de la simulation de ces écoulements, notamment lors des itérations de Newton. Certains choix de variables primaires peuvent être plus appropriés que d'autres.Dans cette thèse, nous cherchons à améliorer la robustesse de la méthode de Newton afin de surmonter les difficultés mentionnées ci-dessus et à proposer des stratégies pour renforcer les conditions de transmission aux interfaces en domaines hétérogènes. Notre travail suit un ordre de difficultés croissantes. Tout d'abord, nous commençons par considérer le modèle le plus simple, l'équation de Richards, dans des milieux homogènes. Ensuite, nous introduisons des hétérogénéités dans le domaine. Enfin, nous considérons le modèle complet dans une configuration difficile : le système diphasique incompressible immiscible dans un domaine hétérogène.Afin d'améliorer la robustesse, nous proposons une stratégie basée sur une bascule de la variable primaire. Elle est facilement implémentée grâce à une variable fictive permettant de décrire à la fois la saturation et la pression, que nous appelons technique de paramétrisation. Les tests numériques effectués confirment le potentiel de cette technique, qui permet de résoudre l'équation de Richards sans se soucier du choix de l'inconnue primaire et sans problème de convergence.Dans un domaine hétérogène, un schéma naïf sans prise en compte explicite des hétérogénéités souffre d'un manque de précision dans les résultats simulés. Cela motive l'introduction d'un traitement spécifique des interfaces. Ainsi, nous proposons et comparons plusieurs approches pour traiter la condition de transmission d'interface, analysant leurs avantages et inconvénients lorsqu'ils sont confrontés à différents paramètres physiques pour l'équation de Richards ainsi que le modèle d'écoulement diphasique de Darcy.
Published: 2021

41. Consistency and Certain Answers in Relational to RDF Data Exchange with Shape Constraints

Author: Boneva, Iovka, Staworko, Lawek, Lozano, Jose, Linking Dynamic Data (LINKS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: FOS: Computer and information sciences, [INFO.INFO-DB]Computer Science [cs]/Databases [cs.DB], Computer Science - Databases, [INFO.INFO-WB]Computer Science [cs]/Web, Databases (cs.DB), Computer Science::Databases
Abstract: We investigate the data exchange from relational databases to RDF graphs inspired by R2RML with the addition of target shape schemas. We study the problems of consistency i.e., checking that every source instance admits a solution, and certain query answering i.e., finding answers present in every solution. We identify the class of constructive relational to RDF data exchange that uses IRI constructors and full tgds (with no existential variables) in its source to target dependencies. We show that the consistency problem is coNP-complete. We introduce the notion of universal simulation solution that allows to compute certain query answers to any class of queries that is robust under simulation. One such class are nested regular expressions (NREs) that are forward i.e., do not use the inverse operation. Using universal simulation solution renders tractable the computation of certain answers to forward NREs (data-complexity). Finally, we present a number of results that show that relaxing the restrictions of the proposed framework leads to an increase in complexity.; rdf
Published: 2021

42. Compactness and structure of zero-states for unoriented Aviles-Giga functionals

Author: Goldman, Michael, Merlet, Benoît, Pegon, Marc, Serfaty, Sylvia, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, and Centre National de la Recherche Scientifique (CNRS)-Université de Lille
Subjects: entropies, vortices, FOS: Physical sciences, Aviles-Giga functional, Mathematical Physics (math-ph), zero-states, Mathematics - Analysis of PDEs, rigidity, 35B36, 35B65, 35J60, 35L65, 49Q20, 49S05, 74G65, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], compactness, Mathematical Physics, Analysis of PDEs (math.AP), disclinations
Abstract: International audience; Motivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles-Giga functional.We introduce a nonlinear curl operator for such unoriented vector fields as well as a family of even entropies which we call "trigonometric entropies". Using these tools we show two main theorems which parallel some results in the literature on the classical Aviles-Giga energy. The first is a compactness result for sequences of configurations with uniformly bounded energies. The second is a complete characterization of zero-states, that is, the limit configurations when the energies go to 0. These are Lipschitz continuous away from a locally finite set of points, near which they form either a vortex pattern or a disclination with degree 1/2. The proof is based on a combination of regularity theory together with techniques coming from the study of the Ginzburg-Landau energy.Our methods provide alternative proofs in the classical Aviles-Giga context.
Published: 2021

43. The Regular Languages of Wire Linear AC 0

Author: Cadilhac, Michaël, Paperman, Charles, School of Computing [DePaul] (SOC), DePaul University [Chicago], Linking Dynamic Data (LINKS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)
Subjects: [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]
Abstract: In this paper, the regular languages of wire linear AC 0 are characterized as the languages expressible in the two-variable fragment of first-order logic with regular predicates, FO 2 [reg]. Additionally, they are characterized as the languages recognized by the algebraic class QLDA. The class is shown to be decidable and examples of languages in and outside of it are presented.
Published: 2021

44. Error analysis for denoising smooth modulo signals on a graph

Author: Tyagi, Hemant, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Tyagi, Hemant, Laboratoire Paul Painlevé - UMR 8524 (LPP), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe
Subjects: FOS: Computer and information sciences, 021103 operations research, Applied Mathematics, 0211 other engineering and technologies, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, 01 natural sciences, 010309 optics, Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0103 physical sciences, FOS: Mathematics, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Abstract: In many applications, we are given access to noisy modulo samples of a smooth function with the goal being to robustly unwrap the samples, i.e., to estimate the original samples of the function. In a recent work, Cucuringu and Tyagi proposed denoising the modulo samples by first representing them on the unit complex circle and then solving a smoothness regularized least squares problem -- the smoothness measured w.r.t the Laplacian of a suitable proximity graph $G$ -- on the product manifold of unit circles. This problem is a quadratically constrained quadratic program (QCQP) which is nonconvex, hence they proposed solving its sphere-relaxation leading to a trust region subproblem (TRS). In terms of theoretical guarantees, $\ell_2$ error bounds were derived for (TRS). These bounds are however weak in general and do not really demonstrate the denoising performed by (TRS). In this work, we analyse the (TRS) as well as an unconstrained relaxation of (QCQP). For both these estimators we provide a refined analysis in the setting of Gaussian noise and derive noise regimes where they provably denoise the modulo observations w.r.t the $\ell_2$ norm. The analysis is performed in a general setting where $G$ is any connected graph., 36 pages, 2 figures. Added Section 5 (Simulations) and made minor changes as per reviewers comments
Published: 2021

45. Computing the Cut Locus of a Riemannian Manifold via Optimal Transport

Author: Enrico Facca, Luca Berti, Francesco Fassò, Mario Putti, Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Padova = University of Padua (Unipd), Laboratoire Paul Painlevé (LPP), Dipartimento di Matematica [Padova], Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), and Universita degli Studi di Padova
Subjects: Mathematics - Differential Geometry, Monge–Kantorovich equations, Optimal Transport problem, Numerical Analysis (math.NA), Cut locus, Differential Geometry (math.DG), Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Numerical Analysis, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Riemannian geometry, [MATH]Mathematics [math], Mathematics - Optimization and Control, geodesic distance, 35J70, 49K20, 49M25, 49Q20, 58J05, 65K10, 65N30, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge–Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver, based on the so-called dynamical Monge–Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in ℝ3, and discuss advantages and limitations.
Published: 2021

46. Progress in Self-Certified Neural Networks

Author: Perez-Ortiz, Maria, Rivasplata, Omar, Parrado-Hernandez, Emilio, Guedj, Benjamin, Shawe-Taylor, John, University College of London [London] (UCL), Universidad Carlos III de Madrid [Madrid] (UC3M), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, The Inria London Programme (Inria-London), Computer science department [University College London] (UCL-CS), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), This work is also supported by the U.S. Army Research Laboratory and the U. S. Army Research Office, and by the U.K. Ministry of Defence and the U.K. Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/R013616/1., European Project: 820437,H2020-EU.1.2.3. - FET Flagships ,Humane AI (2019), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Department of Computer science [University College of London] (UCL-CS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, ComputingMethodologies_PATTERNRECOGNITION, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Machine Learning (cs.LG)
Abstract: A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network models trained by optimising PAC-Bayes bounds lead not only to accurate predictors, but also to tight risk certificates, bearing promise towards achieving self-certified learning. In this context, learning and certification strategies based on PAC-Bayes bounds are especially attractive due to their ability to leverage all data to learn a posterior and simultaneously certify its risk with a tight numerical certificate. In this paper, we assess the progress towards self-certification in probabilistic neural networks learnt by PAC-Bayes inspired objectives. We empirically compare (on 4 classification datasets) classical test set bounds for deterministic predictors and a PAC-Bayes bound for randomised self-certified predictors. We first show that both of these generalisation bounds are not too far from out-of-sample test set errors. We then show that in data starvation regimes, holding out data for the test set bounds adversely affects generalisation performance, while self-certified strategies based on PAC-Bayes bounds do not suffer from this drawback, proving that they might be a suitable choice for the small data regime. We also find that probabilistic neural networks learnt by PAC-Bayes inspired objectives lead to certificates that can be surprisingly competitive with commonly used test set bounds.
Published: 2021

47. Speaker Anonymization: Representation, Evaluation and Formal Guarantees

Author: Srivastava, Brij Mohan Lal, Machine Learning in Information Networks (MAGNET), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Speech Modeling for Facilitating Oral-Based Communication (MULTISPEECH), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Natural Language Processing & Knowledge Discovery (LORIA - NLPKD), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Inria Lille Nord Europe - Laboratoire CRIStAL - Université de Lille, Aurélien Bellet, Emmanuel Vincent and Marc Tommasi, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria), Université de Lille, and Marc Tommasi
Subjects: speaker anonymization, speech, speech recognition, Anonymisation de la voix, vérification du locuteur, privacy, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], parole, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Speech processing, reconnaissance de parole, anonymisation du locuteur, Interfaces vocales, speaker verification, vie privée
Abstract: Large-scale centralized storage of speech data poses severe privacy threats to the speakers. Indeed, the emergence and widespread usage of voice interfaces starting from telephone to mobile applications, and now digital assistants have enabled easier communication between the customers and the service providers. Massive speech data collection allows its users, for instance researchers, to develop tools for human convenience, like voice passwords for banking, personalized smart speakers, etc. However, centralized storage is vulnerable to cybersecurity threats which, when combined with advanced speech technologies like voice cloning, speaker recognition, and spoofing, may endow a malicious entity with the capability to re-identify speakers and breach their privacy by gaining access to their sensitive biometric characteristics, emotional states, personality attributes, pathological conditions, etc. Individuals and the members of civil society worldwide, and especially in Europe, are getting aware of this threat. With firm backing by the GDPR, several initiatives are being launched, including the publication of white papers and guidelines, to spread mass awareness and to regulate voice data so that the citizens' privacy is protected.This thesis is a timely effort to bolster such initiatives and propose solutions to remove the biometric identity of speakers from speech signals, thereby rendering them useless for re-identifying the speakers who spoke them. Besides the goal of protecting the speaker's identity from malicious access, this thesis aims to explore the solutions which do so without degrading the usefulness of speech. We present several anonymization schemes based on voice conversion methods to achieve this two-fold objective. The output of such schemes is a high-quality speech signal that is usable for publication and a variety of downstream tasks. All the schemes are subjected to a rigorous evaluation protocol which is one of the major contributions of this thesis. This protocol led to the finding that the previous approaches do not effectively protect the privacy and thereby directly inspired the VoicePrivacy initiative which is an effort to gather individuals, industry, and the scientific community to participate in building a robust anonymization scheme. We introduce a range of anonymization schemes under the purview of the VoicePrivacy initiative and empirically prove their superiority in terms of privacy protection and utility. Finally, we endeavor to remove the residual speaker identity from the anonymized speech signal using the techniques inspired by differential privacy. Such techniques provide provable analytical guarantees to the proposed anonymization schemes and open up promising perspectives for future research.In practice, the tools developed in this thesis are an essential component to build trust in any software ecosystem where voice data is stored, transmitted, processed, or published. They aim to help the organizations to comply with the rules mandated by civil governments and give a choice to individuals who wish to exercise their right to privacy.; L'émergence et la généralisation des interfaces vocales présentes dans les téléphones, les applications mobiles et les assistants numériques ont permis de faciliter la communication entre les citoyens, utilisateurs d'un service, et les prestataires de services. Citons à titre d'exemple l'utilisation de mots de passe vocaux pour les opérations bancaires, des haut-parleurs intelligents personnalisés, etc. Pour réaliser ces innovations, la collecte massive de données vocales est essentielle aux entreprises comme aux chercheurs. Mais le stockage centralisé à grande échelle des données vocales pose de graves menaces à la vie privée des locuteurs. En effet, le stockage centralisé est vulnérable aux menaces de cybersécurité qui, lorsqu'elles sont combinées avec des technologies vocales avancées telles que le clonage vocal, la reconnaissance du locuteur et l'usurpation d'identité peuvent conférer à une entité malveillante la capacité de ré-identifier les locuteurs et de violer leur vie privée en accédant à leurs caractéristiques biométriques sensibles, leurs états émotionnels, leurs attributs de personnalité, leurs conditions pathologiques, etc. Les individus et les membres de la société civile du monde entier, et particulièrement en Europe, prennent conscience de cette menace. Avec l'entrée en vigueur du règlement général sur la protection des données (RGPD), plusieurs initiatives sont lancées, notamment la publication de livres blancs et de lignes directrices, pour sensibiliser les masses et réguler les données vocales afin que la vie privée des citoyens soit protégée.Cette thèse constitue un effort pour soutenir de telles initiatives et propose des solutions pour supprimer l'identité biométrique des locuteurs des signaux de parole, les rendant ainsi inutiles pour ré-identifier les locuteurs qui les ont prononcés. Outre l'objectif de protéger l'identité du locuteur contre les accès malveillants, cette thèse vise à explorer les solutions qui le font sans dégrader l'utilité de la parole. Nous présentons plusieurs schémas d'anonymisation basés sur des méthodes de conversion vocale pour atteindre ce double objectif. La sortie de tels schémas est un signal vocal de haute qualité qui est utilisable pour la publication et pour un ensemble de tâches en aval. Tous les schémas sont soumis à un protocole d'évaluation rigoureux qui est l'un des apports majeurs de cette thèse. Ce protocole a conduit à la découverte que les approches existantes ne protègent pas efficacement la vie privée et a ainsi directement inspiré l'initiative VoicePrivacy qui rassemble les individus, l'industrie et la communauté scientifique pour participer à la construction d'un schéma d'anonymisation robuste. Nous introduisons une gamme de schémas d'anonymisation dans le cadre de l'initiative VoicePrivacy et prouvons empiriquement leur supériorité en termes de protection de la vie privée et d'utilité. Enfin, nous nous efforçons de supprimer l'identité résiduelle du locuteur du signal de parole anonymisé en utilisant les techniques inspirées de la confidentialité différentielle. De telles techniques fournissent des garanties analytiques démontrables aux schémas d'anonymisation proposés et ouvrent des portes pour de futures recherches.En pratique, les outils développés dans cette thèse sont un élément essentiel pour établir la confiance dans tout écosystème logiciel où les données vocales sont stockées, transmises, traitées ou publiées. Ils visent à aider les organisations à se conformer aux règles mandatées par les gouvernements et à donner le choix aux individus qui souhaitent exercer leur droit à la vie privée.
Published: 2021

48. An exact dynamic programming approach to segmented isotonic regression

Author: Víctor Bucarey, Salvador Pineda, Martine Labbé, Juan M. Morales, Data Analytics Laboratory, Vrije Universiteit Brussel (VUB), Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Département d'informatique [Bruxelles], Université libre de Bruxelles (ULB), Department of Applied Mathematics, Universidad de Málaga [Málaga] = University of Málaga [Málaga], Department of Electrical Engineering, This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovationprogramme (grant agreement no. 755705). This work was also supported in part by the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (ERDF) through project ENE2017-83775-P. Martine Labbé has been partially supported by the Fonds de la Recherche Scientifique - FNRS under Grant(s) no PDR T0098.18., European Project: 755705,FlexAnalytics(2018), University of Málaga, Université libre de Bruxelles (ULB)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)
Subjects: G.4, Mathematical optimization, Information Systems and Management, Computer science, 020209 energy, Strategy and Management, 0211 other engineering and technologies, isotonic regression, Context (language use), 02 engineering and technology, Management Science and Operations Research, Data clustering, Electric power system, Informatique de gestion, Análisis de regresión, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Théorie de la décision et des choix collectifs, segmented regression, Inverse optimization, Mathematics - Optimization and Control, Cardinality-constrained shortest path problem, 90C39, 021103 operations research, consumers' price-response, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], Bidding, Management, Dynamic programming, Data point, Monotone polygon, Smart grid, Segmented regression, inverse optimization, data clustering, Consumers’ price-response, Optimization and Control (math.OC), Curve fitting, Isotonic regression, Recherche opérationnelle
Abstract: This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for samples with thousands of data points in less than a few hours. Furthermore, the algorithm gives a certificate on the optimality gap of any incumbent solution it generates. From a practical standpoint, this piece of research is motivated by the roll-out of smart grids and the increasing role played by the small flexible consumption of electricity in the large-scale integration of renewable energy sources into current power systems. Within this context, our algorithm constitutes an useful tool to generate bidding curves for a pool of small flexible consumers to partake in wholesale electricity markets., SCOPUS: ar.j, info:eu-repo/semantics/published
Published: 2021

49. Tail and quantile estimation for real-valued β-mixing spatial data

Author: TCHAZINO, Tchamiè, Dabo-Niang, Sophie, Diop, Aliou, MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, DAAD et CEA-SMIA, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Tchazino, Tchamiè
Subjects: [STAT]Statistics [stat], functional estimation, spatial dependence, extreme value index, Asymptotic normality, [MATH] Mathematics [math], β-mixing, [MATH]Mathematics [math], bias correction, [STAT] Statistics [stat]
Abstract: This paper deals with extreme-value index estimation of a heavy-tailed distribution of a spatial dependent process. We are particularlyinterested in spatial rare events of a β−mixing process. Given a sta-tionary real-valued multidimensional spatial process {X_i,i ∈ Z^N}, weinvestigate its heavy-tail index estimation. Asymptotic properties ofthe corresponding estimator are established under mildmixingcondi-tions. The particularity of the tail proposed estimator is based on thespatial nature of the sample and its unbiased and reduced variance prop-erties compared to well known tail index estimators. Extreme quantileestimation is also deduced. A numerical study on synthetic and realdatasets is conducted to assess the finite-sample behaviour of the pro-posed estimators.
Published: 2021

50. Towards control of opinion diversity by introducing zealots into a polarised social group

Author: Antoine Vendeville, Benjamin Guedj, Shi Zhou, Computer science department [University College London] (UCL-CS), University College of London [London] (UCL), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Department of Computer science [University College of London] (UCL-CS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Laboratoire Paul Painlevé - UMR 8524 (LPP), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe
Subjects: Social and Information Networks (cs.SI), FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], 0103 physical sciences, Computer Science - Social and Information Networks, 16. Peace & justice, 010306 general physics, 01 natural sciences, [INFO.INFO-SI]Computer Science [cs]/Social and Information Networks [cs.SI], Machine Learning (cs.LG), 010305 fluids & plasmas
Abstract: We explore a method to influence or even control the diversity of opinions within a polarised social group. We leverage the voter model in which users hold binary opinions and repeatedly update their beliefs based on others they connect with. Stubborn agents who never change their minds ("zealots") are also disseminated through the network, which is modelled by a connected graph. Building on earlier results, we provide a closed-form expression for the average opinion of the group at equilibrium. This leads us to a strategy to inject zealots into a polarised network in order to shift the average opinion towards any target value. We account for the possible presence of a backfire effect, which may lead the group to react negatively and reinforce its level of polarisation in response. Our results are supported by numerical experiments on synthetic data., 14 pages, 4 figures
Published: 2021

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