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49 results on '"Couellan , Nicolas"'

1. Cartan moving frames and the data manifolds

Author

Tron, Eliot, Fioresi, Rita, Couellan, Nicolas, and Puechmorel, Stéphane

Subjects
Statistics - Machine Learning, Computer Science - Machine Learning, Mathematics - Differential Geometry
Abstract

The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output classes that are easily reachable from a given input. This emphasizes how the proposed mathematical relationship between the output of the network and the geometry of its inputs can be exploited as an explainable artificial intelligence tool.

Published
2024
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3. MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem

Author

Sbihi, Mohammed, Jan, Sophie, and Couellan, Nicolas

Subjects
Mathematics - Optimization and Control, Statistics - Machine Learning
Abstract

It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.

Published
2024

5. Distributional loss for convolutional neural network regression and application to GNSS multi-path estimation

Author

Gonzalez, Thomas, Blais, Antoine, Couëllan, Nicolas, and Ruiz, Christian

Subjects
Computer Science - Computer Vision and Pattern Recognition, Electrical Engineering and Systems Science - Signal Processing
Abstract

Convolutional Neural Network (CNN) have been widely used in image classification. Over the years, they have also benefited from various enhancements and they are now considered as state of the art techniques for image like data. However, when they are used for regression to estimate some function value from images, fewer recommendations are available. In this study, a novel CNN regression model is proposed. It combines convolutional neural layers to extract high level features representations from images with a soft labelling technique. More specifically, as the deep regression task is challenging, the idea is to account for some uncertainty in the targets that are seen as distributions around their mean. The estimations are carried out by the model in the form of distributions. Building from earlier work, a specific histogram loss function based on the Kullback-Leibler (KL) divergence is applied during training. The model takes advantage of the CNN feature representation and is able to carry out estimation from multi-channel input images. To assess and illustrate the technique, the model is applied to Global Navigation Satellite System (GNSS) multi-path estimation where multi-path signal parameters have to be estimated from correlator output images from the I and Q channels. The multi-path signal delay, magnitude, Doppler shift frequency and phase parameters are estimated from synthetically generated datasets of satellite signals. Experiments are conducted under various receiving conditions and various input images resolutions to test the estimation performances quality and robustness. The results show that the proposed soft labelling CNN technique using distributional loss outperforms classical CNN regression under all conditions. Furthermore, the extra learning performance achieved by the model allows the reduction of input image resolution from 80x80 down to 40x40 or sometimes 20x20.

Published
2022

7. Adversarial attacks on neural networks through canonical Riemannian foliations

Author

Tron, Eliot, Couellan, Nicolas, and Puechmorel, Stéphane

Subjects
Statistics - Machine Learning, Computer Science - Information Theory, Computer Science - Machine Learning, Mathematics - Differential Geometry
Abstract

Deep learning models are known to be vulnerable to adversarial attacks. Adversarial learning is therefore becoming a crucial task. We propose a new vision on neural network robustness using Riemannian geometry and foliation theory. The idea is illustrated by creating a new adversarial attack that takes into account the curvature of the data space. This new adversarial attack, called the two-step spectral attack is a piece-wise linear approximation of a geodesic in the data space. The data space is treated as a (degenerate) Riemannian manifold equipped with the pullback of the Fisher Information Metric (FIM) of the neural network. In most cases, this metric is only semi-definite and its kernel becomes a central object to study. A canonical foliation is derived from this kernel. The curvature of transverse leaves gives the appropriate correction to get a two-step approximation of the geodesic and hence a new efficient adversarial attack. The method is first illustrated on a 2D toy example in order to visualize the neural network foliation and the corresponding attacks. Next, we report numerical results on the MNIST and CIFAR10 datasets with the proposed technique and state of the art attacks presented in Zhao et al. (2019) (OSSA) and Croce et al. (2020) (AutoAttack). The result show that the proposed attack is more efficient at all levels of available budget for the attack (norm of the attack), confirming that the curvature of the transverse neural network FIM foliation plays an important role in the robustness of neural networks. The main objective and interest of this study is to provide a mathematical understanding of the geometrical issues at play in the data space when constructing efficient attacks on neural networks.

Published
2022
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8. Robust SVM Optimization in Banach spaces

Author

Sbihi, Mohammed and Couellan, Nicolas

Subjects
Statistics - Machine Learning, Computer Science - Machine Learning, Mathematics - Optimization and Control
Abstract

We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation. Furthermore, we propose a game theoretic interpretation by expressing a Nash equilibrium problem formulation for the more general problem of finding the closest points in two closed convex sets when the underlying space is reflexive and smooth., Comment: 20 pages

Published
2022

10. LRP-GUS: A Visual Based Data Reduction Algorithm for Neural Networks

Author

Guibert, Arnaud, Hurter, Christophe, Couellan, Nicolas, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Iliadis, Lazaros, editor, Papaleonidas, Antonios, editor, Angelov, Plamen, editor, and Jayne, Chrisina, editor

Published
2023
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11. A statistical approach for robust tolerance design

Author

Diet, Ambre, Couellan, Nicolas, Gendre, Xavier, and Martin, Julien

Subjects
Statistics - Applications
Abstract

Within an industrial manufacturing process, tolerancing is a key player. The dimensions uncertainties management starts during the design phase, with an assessment on variability of parts not yet produced. For one assembly step, we can gain knowledge from the tolerance range required for the parts involved. In order to assess output uncertainty of this assembly in a reliable way, this paper presents an approach based on the deviation of the sum of uniform distributions. As traditional approaches based on Hoeffding inequalities do not give accurate results when the deviation considered is small, we propose an improved upper bound. We then discuss how the stack chain geometry impacts the bound definition. Finally, we show an application of the proposed approach in tolerance design of an aircraft sub-assembly. The main interest of the technique compared to existing methodologies is the management of the confidence level and the emphasis of the explicit role of the balance within the stack chain.

Published
2019

12. Convolutional Neural Network for Multipath Detection in GNSS Receivers

Author

Munin, Evgenii, Blais, Antoine, and Couellan, Nicolas

Subjects
Electrical Engineering and Systems Science - Signal Processing, Statistics - Machine Learning
Abstract

Global Navigation Satellite System (GNSS) signals are subject to different kinds of events causing significant errors in positioning. This work explores the application of Machine Learning (ML) methods of anomaly detection applied to GNSS receiver signals. More specifically, our study focuses on multipath contamination, using samples of the correlator output signal. The GPS L1 C/A signal data is used and sourced directly from the correlator output. To extract the important features and patterns from such data, we use deep convolutional neural networks (CNN), which have proven to be efficient in image analysis in particular. To take advantage of CNN, the correlator output signal is mapped as a 2D input image and fed to the convolutional layers of a neural network. The network automatically extracts the relevant features from the input samples and proceeds with the multipath detection. We train the CNN using synthetic signals. To optimize the model architecture with respect to the GNSS correlator complexity, the evaluation of the CNN performance is done as a function of the number of correlator output points.

Published
2019

13. The coupling effect of Lipschitz regularization in deep neural networks

Author

Couellan, Nicolas

Subjects
Computer Science - Machine Learning, Statistics - Machine Learning
Abstract

We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight the fact that this regularization is not only a way to control the magnitude of the weights but has also a coupling effect on the network weights accross the layers. We claim and show evidence on a dataset that this coupling effect brings a tradeoff between robustness and expressiveness of the network. This suggests that Lipschitz regularization should be carefully implemented so as to maintain coupling accross layers.

Published
2019

16. Feature uncertainty bounding schemes for large robust nonlinear SVM classifiers

Author

Couellan, Nicolas and Jan, Sophie

Subjects
Statistics - Machine Learning, Computer Science - Learning
Abstract

We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to random approximate features in low dimensional spaces. The proposed techniques are based on Random Fourier Features and the Nystr\"om methods. The resulting formulations can be solved with efficient stochastic approximation techniques such as stochastic (sub)-gradient, stochastic proximal gradient techniques or their variants.

Published
2017

23. A time-dependent subgraph-capacity model for multiple shortest paths and application to CO2/contrail-safe aircraft trajectories

Author

Demouge, Céline, Mongeau, Marcel, Couellan, Nicolas, Delahaye, Daniel, ENAC - Equipe Optim (OPTIM), Ecole Nationale de l'Aviation Civile (ENAC), 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), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mixed Integer Linear Programming, Subgraph constrained time-dependent shortest path problem, Contrails, [INFO]Computer Science [cs], [MATH]Mathematics [math], Air transportation
Abstract

This paper proposes a study motivated by the problem of minimizing the environmental impact of air transport at the level of a complete air network, considering thereby several aircraft. Both CO2 and non-CO2 effects are taken into account to calculate this impact. The proposed methodology takes into account a network point of view where airspace capacities evolve as well as the traffic itself over time. Finding a shortest path with various constraints and cost functions is a common problem in operations research. This particular study deals with the special case of computing multiple shortest paths with capacity constraints on a time-dependent subgraph. Multiple shortest paths is understood as one shortest path for each vehicle considered. The static special case is modeled as a Mixed Integer Linear Program (MILP), so that it can be solved directly by a standard commercial solver. The time-dependent nature of the problem is then modeled thanks to a sliding-window approach. Encouraging numerical results on the CO2/contrail-safe aircraft trajectories application are obtained and show that the environmental impact can be significantly reduced while maintaining safety by satisfying the airspace capacity constraints.

Published
2023

27. Modèle paramétrique pour estimer la dégradation de la fiabilité de démarrage d’une turbine à gaz à partir de données d’essais

Author

Asoyan, Artashes, Bondivenne, Eric, Couellan, Nicolas, Humbert, Sophie, Klein, Thierry, Safran Helicopter Engines, Ecole Nationale de l'Aviation Civile (ENAC), 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), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[STAT]Statistics [stat], modèle paramétrique de dégradation, maximum de vraisemblance, données d’essais, probit, fiabilité, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], robustesse
Abstract

National audience; L’objectif de cette étude est d’estimer la probabilité de démarrage d’un turbomoteur en tout point de l’espace des facteurs jugés influents. En l’absence de modèle physique du démarrage et de nombre limité de données, une méthode générale d’estimation de la probabilité de démarrage à travers un modèle de dégradation paramétrique est proposée. Le modèle est régi par la distance à un point où la probabilité de démarrage est 1. La sélection du modèle revient à estimer la matrice définissant la distance dans l’espace des facteurs influents. Cette matrice est estimée par maximum de vraisemblance. Une application industrielle à partir des données d’essais de turbomoteur d’hélicoptère est présentée. Les résultats numériques sont prometteurs mais ont montré qu’il est nécessaire de considérer une classe plus générique de modèle. Enfin à travers une étude de robustesse, le modèle a aussi montré une stabilité à des faibles perturbations des données d’essais.

Published
2022

28. Canonical foliations of neural networks: application to robustness

Author

Tron, Eliot, Couellan, Nicolas, Puechmorel, Stéphane, Ecole normale supérieure de Lyon (Ens Lyon), Ecole Nationale de l'Aviation Civile (ENAC), 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), and ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019)

Subjects
FOS: Computer and information sciences, Mathematics - Differential Geometry, Computer Science - Machine Learning, Neural Networks, Information Theory (cs.IT), Computer Science - Information Theory, Adversarial attacks, Machine Learning (stat.ML), Machine Learning (cs.LG), Differential Geometry (math.DG), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Fisher Information Metric, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, Mathematics::Differential Geometry, Robustness, Information geometry, Computer Science::Cryptography and Security
Abstract

Deep learning models are known to be vulnerable to adversarial attacks. Adversarial learning is therefore becoming a crucial task. We propose a new vision on neural network robustness using Riemannian geometry and foliation theory. The idea is illustrated by creating a new adversarial attack that takes into account the curvature of the data space. This new adversarial attack called the two-step spectral attack is a piece-wise linear approximation of a geodesic in the data space. The data space is treated as a (degenerate) Riemannian manifold equipped with the pullback of the Fisher Information Metric (FIM) of the neural network. In most cases, this metric is only semi-definite and its kernel becomes a central object to study. A canonical foliation is derived from this kernel. The curvature of transverse leaves gives the appropriate correction to get a two-step approximation of the geodesic and hence a new efficient adversarial attack. The method is first illustrated on a 2D toy example in order to visualize the neural network foliation and the corresponding attacks. Next, experiments on the MNIST dataset with the proposed technique and a state of the art attack presented in Zhao et al. (2019) are reported. The result show that the proposed attack is more efficient at all levels of available budget for the attack (norm of the attack), confirming that the curvature of the transverse neural network FIM foliation plays an important role in the robustness of neural networks.

Published
2022

31. A dynamic subgraph-capacity model for multiple shortest paths and application to CO2/contrail-safe aircraft trajectories

Author

Demouge, Céline, Mongeau, Marcel, Couellan, Nicolas, Delahaye, Daniel, Demouge, Céline, ENAC - Equipe Optim (OPTIM), Ecole Nationale de l'Aviation Civile (ENAC), 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), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mixed Integer Linear Programming, Subgraph constrained time-dependent shortest path problem Contrails Air transportation Mixed Integer Linear Programming, Subgraph constrained time-dependent shortest path problem, Contrails, [INFO]Computer Science [cs], [MATH] Mathematics [math], [MATH]Mathematics [math], [INFO] Computer Science [cs], Air transportation
Abstract

Finding a shortest path with various constraints and cost functions is a common problem in operations research. This paper deals with the special case of the problem of computing multiple shortest paths with capacity constraints on a subgraph that evolves over time. Multiple shortest paths is understood as paths for each vehicle considered. The static special case is modeled as a Mixed Integer Linear Programming (MILP) problem, so that it can be solved directly by a standard commercial solver. The time-dependent nature of the problem is then modeled thanks to a sliding-window approach. This study is motivated by the problem of minimizing the environmental impact of air transport at the level of a complete air network, considering thereby several aircraft. Both CO2 and non-CO2 effects are taken into account to calculate the impact. The proposed methodology takes into account a network point of view where airspace (subgraph) capacities evolve as well as the traffic itself over time. Encouraging numerical results on the CO2 /contrail-safe aircraft trajectories application are obtained and show that the environmental impact can be reduced while maintaining safety by guaranteeing the respect of airspace capacities.

Published
2022

35. Using Wasserstein-2 regularization to ensure fair decisions with Neural-Network classifiers

Author

Risser, Laurent, Vincenot, Quentin, Couellan, Nicolas, Loubes, Jean-Michel, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), 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), Centre d'Etudes des Langues et Littératures Anciennes et Modernes (CELLAM), Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES), Ecole Nationale de l'Aviation Civile (ENAC), 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), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH]Mathematics [math]
Abstract

In this paper, we propose a new method to build fair Neural-Network classifiers by using a constraint based on the Wasserstein distance. More specifically, we detail how to efficiently compute the gradients of Wasserstein-2 regularizers for Neural-Networks. The proposed strategy is then used to train Neural-Networks decision rules which favor fair predictions. Our method fully takes into account two specificities of Neural-Networks training: (1) The network parameters are indirectly learned based on automatic differentiation and on the loss gradients, and (2) batch training is the gold standard to approximate the parameter gradients, as it requires a reasonable amount of computations and it can efficiently explore the parameters space. Results are shown on synthetic data, as well as on the UCI Adult Income Dataset. Our method is shown to perform well compared with 'ZafarICWWW17' and linear-regression with Wasserstein-1 regularization, as in 'JiangUAI19', in particular when non-linear decision rules are required for accurate predictions.

Published
2019

37. On the convergence of a stochastic approximation method for structured bi-level optimization

Author

Couellan , Nicolas, Wang , Wenjuan, Ecole Nationale de l'Aviation Civile (ENAC), 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), Bournemouth University [Poole] (BU), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), 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), Ecole Nationale de l'Aviation Civile ( ENAC ), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), and Bournemouth University [Poole] ( BU )

Subjects
[ MATH ] Mathematics [math], [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [ INFO.INFO-LG ] Computer Science [cs]/Machine Learning [cs.LG]
Abstract

We analyze the convergence of stochastic gradient methods for well structured bi-level optimization problems. We address two specific cases: first when the outer objective function can be expressed as a finite sum of independent terms, and next when both the outer and inner objective functions can be expressed as finite sums of independent terms. We assume Lipschitz continuity and differentiability of both objectives as well as convexity of the inner objective and consider diminishing steps sizes. We show that, under these conditions and some other assumptions on the implicit function and the variance of the gradient errors, both methods converge in expectation to a stationary point of the problem if gradient approximations are chosen so as to satisfy a sufficient decrease condition. We also discuss the satisfaction of our assumptions in machine learning problems where these methods can be nicely applied to automatically tune hyperparameters when the loss functions are very large sums of error terms.

Published
2018

39. Report on CIMI Thematic Trimester: Machine Learning

Author

Afantenos, Stergos, Couellan, Nicolas, Garivier, Aurélien, Gerchinovitz, Sébastien, Loubes, Jean-Michel, Malgouyres, François, Mothe, Josiane, Mouysset, Sandrine, Pauwels, Edouard, Serrurier, Mathieu, Van De Cruys, Tim, MEthodes et ingénierie des Langues, des Ontologies et du DIscours (IRIT-MELODI), Institut de recherche en informatique de Toulouse (IRIT), 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 Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse III - Paul Sabatier (UT3), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Systèmes d’Informations Généralisées (IRIT-SIG), Université Toulouse - Jean Jaurès (UT2J), Algorithmes Parallèles et Optimisation (IRIT-APO), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), IRIT : Institut de Recherche en Informatique de Toulouse, ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-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 Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), 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)-Centre National de la Recherche Scientifique (CNRS), Grélaud, Françoise, and Centre International de Mathématiques et d'Informatique (de Toulouse) - - CIMI2011 - ANR-11-LABX-0040 - LABX - VALID

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], SIGEVI, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Published
2016

41. A Natural Formalism and a Multi-Agent Algorithm for Integrative Multidisciplinary Design Optimization (Workshop @ AAMAS 2013)

Author

Jorquera, Tom, Georgé, Jean-Pierre, Gleizes, Marie-Pierre, Couellan, Nicolas, Noël, Victor, Régis, Christine, Grélaud, Françoise, Systèmes Multi-Agents Coopératifs (IRIT-SMAC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-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 Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Multi-Agent System, [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], Self-Adaptation, [INFO.INFO-MA] Computer Science [cs]/Multiagent Systems [cs.MA], Integrative Design, Multidisciplinary Optimization
Abstract

International audience; MultiDisciplinary Optimization (MDO) problems represent one of the hardest and broadest domains of continuous optimization. By involving both the models and criteria of different disciplines, MDO problems are often too complex to be tackled by classical optimization methods. We propose an approach for taking into account this complexity using a new formalism (NDMO - Natural Domain Modeling for Optimization) and a self-adaptive multi-agent algorithm. Our method agentifies the different elements of the problem (such as the variables, the models, the objectives). Each agent is in charge of a small part of the problem and cooperates with its neighbors to find equilibrium on conflicting values. Despite the fact that no agent of the system has a complete view of the entire problem, the mechanisms we provide make the emergence of a coherent solution possible. Evaluations on several academic and industrial test cases are provided.

Published
2013

47. Affine scaling neural network training algorithm for prediction of tornados

Author

Theodore Trafalis, Couellan, Nicolas P., Li, Po-I, Stumpf, Greg, White, Anderson, COUELLAN, Nicolas, University of Oklahoma (OU), National Severe Storms Laboratory (NSSL), and National Oceanic and Atmospheric Administration (NOAA)

Subjects
[SDU.STU.ME] Sciences of the Universe [physics]/Earth Sciences/Meteorology, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [SDU.STU.ME]Sciences of the Universe [physics]/Earth Sciences/Meteorology, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

48. Primal-dual techniques for nonlinear programming and applications to artificial neural network training.

Author

Couellan, Nicolas P.

Subjects
Computer Science., Neural networks (Computer science), Linear programming., Engineering, Industrial., Engineering, System Science.
Abstract

In this work, new developments in primal-dual techniques for general constrained non-linear programming problems are proposed. We first implement a modified version of the general nonlinear primal-dual algorithm that was published by El-Bakry et al. (21). We use the algorithm as a backbone of a new stochastic hybrid technique for solving general constrained nonlinear programming problems. The idea is to combine a fast local optimization strategy and a global search technique. The technique is a modified nonlinear primal-dual technique that uses concepts from simulated annealing to increase the probability of converging to the global minima of the objective function. At each iteration, the algorithm solves the Karush-Kuhn-Tucker optimality conditions to find the next iterate. A random noise is added to the resulting direction of move in order to escape local minima. The noise is gradually removed throughout the iteration process. We show that for complicated problems that possess numerous local minima and global minima, the proposed algorithm outperforms the deterministic approach. We also develop a new class of incremental nonlinear primal-dual techniques for solving optimization problems with special decomposition properties. Specifically, the objective functions of the problems are sums of independent nonconvex differentiable terms minimized subject to a set of nonlinear constraints for each term. The technique performs successive primal-dual increments for each decomposition term of the objective function. The method is particularly beneficial for online applications and problems that have a large amount of data. We show that the technique can be nicely applied to artificial neural training and provide experimental results for financial forecasting problems.

Published
1997

49. Neural Network training via a primal-dual interior point method for nonlinear programming

Author

Nicolas Couellan, Trafalis, Theodore B., University of Oklahoma (OU), and COUELLAN, Nicolas

Subjects
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
1994

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