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We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle.

At the same time that artificial intelligence is becoming popular, concern and the need for regulation is growing, including among other requirements the data privacy. In this context, Federated Learning is proposed as a solution to data privacy concerns derived from different source data scenarios due to its distributed learning. The defense mechanisms proposed in literature are just focused on defending against adversarial attacks and the performance, leaving aside other important qualities such as explainability, fairness to poor quality clients, dynamism in terms of attacks configuration and generality in terms of being resilient against different kinds of attacks. In this work, we propose RAB$^2$-DEF, a $\textbf{r}$esilient $\textbf{a}$gainst $\textbf{b}\text{yzantine}$ and $\textbf{b}$ackdoor attacks which is $\textbf{d}$ynamic, $\textbf{e}$xplainable and $\textbf{f}$air to poor clients using local linear explanations. We test the performance of RAB$^2$-DEF in image datasets and both byzantine and backdoor attacks considering the state-of-the-art defenses and achieve that RAB$^2$-DEF is a proper defense at the same time that it boosts the other qualities towards trustworthy artificial intelligence.

Transformers have become the leading choice in natural language processing over other deep learning architectures. This trend has also permeated the field of time series analysis, especially for long-horizon forecasting, showcasing promising results both in performance and running time. In this paper, we introduce Local Attention Mechanism (LAM), an efficient attention mechanism tailored for time series analysis. This mechanism exploits the continuity properties of time series to reduce the number of attention scores computed. We present an algorithm for implementing LAM in tensor algebra that runs in time and memory O(nlogn), significantly improving upon the O(n^2) time and memory complexity of traditional attention mechanisms. We also note the lack of proper datasets to evaluate long-horizon forecast models. Thus, we propose a novel set of datasets to improve the evaluation of models addressing long-horizon forecasting challenges. Our experimental analysis demonstrates that the vanilla transformer architecture magnified with LAM surpasses state-of-the-art models, including the vanilla attention mechanism. These results confirm the effectiveness of our approach and highlight a range of future challenges in long-sequence time series forecasting.

In the last few years, the formulation of real-world optimization problems and their efficient solution via metaheuristic algorithms has been a catalyst for a myriad of research studies. In spite of decades of historical advancements on the design and use of metaheuristics, large difficulties still remain in regards to the understandability, algorithmic design uprightness, and performance verifiability of new technical achievements. A clear example stems from the scarce replicability of works dealing with metaheuristics used for optimization, which is often infeasible due to ambiguity and lack of detail in the presentation of the methods to be reproduced. Additionally, in many cases, there is a questionable statistical significance of their reported results. This work aims at providing the audience with a proposal of good practices which should be embraced when conducting studies about metaheuristics methods used for optimization in order to provide scientific rigor, value and transparency. To this end, we introduce a step by step methodology covering every research phase that should be followed when addressing this scientific field. Specifically, frequently overlooked yet crucial aspects and useful recommendations will be discussed in regards to the formulation of the problem, solution encoding, implementation of search operators, evaluation metrics, design of experiments, and considerations for real-world performance, among others. Finally, we will outline important considerations, challenges, and research directions for the success of newly developed optimization metaheuristics in their deployment and operation over real-world application environments.

Early detection of diseases in crops is essential to prevent harvest losses and improve the quality of the final product. In this context, the combination of machine learning and proximity sensors is emerging as a technique capable of achieving this detection efficiently and effectively. For example, this machine learning approach has been applied to potato crops -- to detect late blight (Phytophthora infestans) -- and grapevine crops -- to detect downy mildew. However, most of these AI models found in the specialised literature have been developed using leaf-by-leaf images taken in the lab, which does not represent field conditions and limits their applicability. In this study, we present the first machine learning model capable of detecting mild symptoms of late blight in potato crops through the analysis of high-resolution RGB images captured directly in the field, overcoming the limitations of other publications in the literature and presenting real-world applicability. Our proposal exploits the availability of high-resolution images via the concept of patching, and is based on deep convolutional neural networks with a focal loss function, which makes the model to focus on the complex patterns that arise in field conditions. Additionally, we present a data augmentation scheme that facilitates the training of these neural networks with few high-resolution images, which allows for development of models under the small data paradigm. Our model correctly detects all cases of late blight in the test dataset, demonstrating a high level of accuracy and effectiveness in identifying early symptoms. These promising results reinforce the potential use of machine learning for the early detection of diseases and pests in agriculture, enabling better treatment and reducing their impact on crops., Comment: 9 pages

One of the key issues regarding classification problems in Trustworthy Artificial Intelligence is ensuring Fairness in the prediction of different classes when protected (sensitive) features are present. Data quality is critical in these cases, as biases in training data can be reflected in machine learning, impacting human lives and failing to comply with current regulations. One strategy to improve data quality and avoid these problems is preprocessing the dataset. Instance selection via undersampling can foster balanced learning of classes and protected feature values. Performing undersampling in class overlap areas close to the decision boundary should bolster the impact on the classifier. This work proposes Fair Overlap Number of Balls (Fair-ONB), an undersampling method that harnesses the data morphology of the different data groups (obtained from the combination of classes and protected feature values) to perform guided undersampling in overlap areas. It employs attributes of the ball coverage of the groups, such as the radius, number of covered instances and density, to select the most suitable areas for undersampling and reduce bias. Results show that the Fair-ONB method improves model Fairness with low impact on the classifier's predictive performance., Comment: 14 pages, 5 tables, 8 figures

Significant advancements in the field of wood species identification are needed worldwide to support sustainable timber trade. In this work we contribute to automate the identification of wood species via high-resolution macroscopic images of timber. The main challenge of this problem is that fine-grained patterns in timber are crucial in order to accurately identify wood species, and these patterns are not properly learned by traditional convolutional neural networks (CNNs) trained on low/medium resolution images. We propose a Timber Deep Learning Identification with Patch-based Inference Voting methodology, abbreviated TDLI-PIV methodology. Our proposal exploits the concept of patching and the availability of high-resolution macroscopic images of timber in order to overcome the inherent challenges that CNNs face in timber identification. The TDLI-PIV methodology is able to capture fine-grained patterns in timber and, moreover, boosts robustness and prediction accuracy via a collaborative voting inference process. In this work we also introduce a new data set of marcroscopic images of timber, called GOIMAI-Phase-I, which has been obtained using optical magnification in order to capture fine-grained details, which contrasts to the other datasets that are publicly available. More concretely, images in GOIMAI-Phase-I are taken with a smartphone with a 24x magnifying lens attached to the camera. Our data set contains 2120 images of timber and covers 37 legally protected wood species. Our experiments have assessed the performance of the TDLI-PIV methodology, involving the comparison with other methodologies available in the literature, exploration of data augmentation methods and the effect that the dataset size has on the accuracy of TDLI-PIV., Comment: 17 pages and 6 figures

In Artificial Intelligence, there is an increasing demand for adaptive models capable of dealing with a diverse spectrum of learning tasks, surpassing the limitations of systems devised to cope with a single task. The recent emergence of General-Purpose Artificial Intelligence Systems (GPAIS) poses model configuration and adaptability challenges at far greater complexity scales than the optimal design of traditional Machine Learning models. Evolutionary Computation (EC) has been a useful tool for both the design and optimization of Machine Learning models, endowing them with the capability to configure and/or adapt themselves to the task under consideration. Therefore, their application to GPAIS is a natural choice. This paper aims to analyze the role of EC in the field of GPAIS, exploring the use of EC for their design or enrichment. We also match GPAIS properties to Machine Learning areas in which EC has had a notable contribution, highlighting recent milestones of EC for GPAIS. Furthermore, we discuss the challenges of harnessing the benefits of EC for GPAIS, presenting different strategies to both design and improve GPAIS with EC, covering tangential areas, identifying research niches, and outlining potential research directions for EC and GPAIS.

Motivated by work of Dolgopyat and N\'andori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions. Building on previous work of Al-Saqban and Forni, we apply this method to obtain mixing limit theorems for particular subbundles of the Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar these results are applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces., Comment: 45 pages

Explainable Artificial Intelligence (XAI) is a pivotal research domain aimed at understanding the operational mechanisms of AI systems, particularly those considered ``black boxes'' due to their complex, opaque nature. XAI seeks to make these AI systems more understandable and trustworthy, providing insight into their decision-making processes. By producing clear and comprehensible explanations, XAI enables users, practitioners, and stakeholders to trust a model's decisions. This work analyses the value of data morphology strategies in generating counterfactual explanations. It introduces the Overlap Number of Balls Model-Agnostic CounterFactuals (ONB-MACF) method, a model-agnostic counterfactual generator that leverages data morphology to estimate a model's decision boundaries. The ONB-MACF method constructs hyperspheres in the data space whose covered points share a class, mapping the decision boundary. Counterfactuals are then generated by incrementally adjusting an instance's attributes towards the nearest alternate-class hypersphere, crossing the decision boundary with minimal modifications. By design, the ONB-MACF method generates feasible and sparse counterfactuals that follow the data distribution. Our comprehensive benchmark from a double perspective (quantitative and qualitative) shows that the ONB-MACF method outperforms existing state-of-the-art counterfactual generation methods across multiple quality metrics on diverse tabular datasets. This supports our hypothesis, showcasing the potential of data-morphology-based explainability strategies for trustworthy AI., Comment: 21 pages, 6 figures. Submitted to Information Sciences

In the realm of Artificial Intelligence (AI), the need for privacy and security in data processing has become paramount. As AI applications continue to expand, the collection and handling of sensitive data raise concerns about individual privacy protection. Federated Learning (FL) emerges as a promising solution to address these challenges by enabling decentralized model training on local devices, thus preserving data privacy. This paper introduces FLEX: a FLEXible Federated Learning Framework designed to provide maximum flexibility in FL research experiments. By offering customizable features for data distribution, privacy parameters, and communication strategies, FLEX empowers researchers to innovate and develop novel FL techniques. The framework also includes libraries for specific FL implementations including: (1) anomalies, (2) blockchain, (3) adversarial attacks and defences, (4) natural language processing and (5) decision trees, enhancing its versatility and applicability in various domains. Overall, FLEX represents a significant advancement in FL research, facilitating the development of robust and efficient FL applications., Comment: Submitted to Information Fusion

As Artificial Intelligence systems become integral across domains, the demand for explainability grows. While the effort by the scientific community is focused on obtaining a better explanation for the model, it is important not to ignore the potential of this explanation process to improve training as well. While existing efforts primarily focus on generating and evaluating explanations for black-box models, there remains a critical gap in directly enhancing models through these evaluations. This paper introduces SHIELD (Selective Hidden Input Evaluation for Learning Dynamics), a regularization technique for explainable artificial intelligence designed to improve model quality by concealing portions of input data and assessing the resulting discrepancy in predictions. In contrast to conventional approaches, SHIELD regularization seamlessly integrates into the objective function, enhancing model explainability while also improving performance. Experimental validation on benchmark datasets underscores SHIELD's effectiveness in improving Artificial Intelligence model explainability and overall performance. This establishes SHIELD regularization as a promising pathway for developing transparent and reliable Artificial Intelligence regularization techniques., Comment: 18 pages, 8 figures

Trustworthy Artificial Intelligence solutions are essential in today's data-driven applications, prioritizing principles such as robustness, safety, transparency, explainability, and privacy among others. This has led to the emergence of Federated Learning as a solution for privacy and distributed machine learning. While decision trees, as self-explanatory models, are ideal for collaborative model training across multiple devices in resource-constrained environments such as federated learning environments for injecting interpretability in these models. Decision tree structure makes the aggregation in a federated learning environment not trivial. They require techniques that can merge their decision paths without introducing bias or overfitting while keeping the aggregated decision trees robust and generalizable. In this paper, we propose an Interpretable Client Decision Tree Aggregation process for Federated Learning scenarios that keeps the interpretability and the precision of the base decision trees used for the aggregation. This model is based on aggregating multiple decision paths of the decision trees and can be used on different decision tree types, such as ID3 and CART. We carry out the experiments within four datasets, and the analysis shows that the tree built with the model improves the local models, and outperforms the state-of-the-art., Comment: Submitted to Information Science Journal

Social Media and Internet have the potential to be exploited as a source of opinion to enrich Decision Making solutions. Crowd Decision Making (CDM) is a methodology able to infer opinions and decisions from plain texts, such as reviews published in social media platforms, by means of Sentiment Analysis. Currently, the emergence and potential of Large Language Models (LLMs) lead us to explore new scenarios of automatically understand written texts, also known as natural language processing. This paper analyzes the use of ChatGPT based on prompt design strategies to assist in CDM processes to extract opinions and make decisions. We integrate ChatGPT in CDM processes as a flexible tool that infer the opinions expressed in texts, providing numerical or linguistic evaluations where the decision making models are based on the prompt design strategies. We include a multi-criteria decision making scenario with a category ontology for criteria. We also consider ChatGPT as an end-to-end CDM model able to provide a general opinion and score on the alternatives. We conduct empirical experiments on real data extracted from TripAdvisor, the TripR-2020Large dataset. The analysis of results show a promising branch for developing quality decision making models using ChatGPT. Finally, we discuss the challenges of consistency, sensitivity and explainability associated to the use of LLMs in CDM processes, raising open questions for future studies.

Classic Delphi and Fuzzy Delphi methods are used to test content validity of a data collection tools such as questionnaires. Fuzzy Delphi takes the opinion issued by judges from a linguistic perspective reducing ambiguity in opinions by using fuzzy numbers. We propose an extension named 2-Tuple Fuzzy Linguistic Delphi method to deal with scenarios in which judges show different expertise degrees by using fuzzy multigranular semantics of the linguistic terms and to obtain intermediate and final results expressed by 2-tuple linguistic values. The key idea of our proposal is to validate the full questionnaire by means of the evaluation of its parts, defining the validity of each item as a Decision Making problem. Taking the opinion of experts, we measure the degree of consensus, the degree of consistency, and the linguistic score of each item, in order to detect those items that affect, positively or negatively, the quality of the instrument. Considering the real need to evaluate a b-learning educational experience with a consensual questionnaire, we present a Decision Making model for questionnaire validation that solve it. Additionally, we contribute to this consensus reaching problem by developing an online tool under GPL v3 license. The software visualizes the collective valuations for each iteration and assists to determine which parts of the questionnaire should be modified to reach a consensual solution., Comment: project at https://github.com/rosanamontes/teranga.go. arXiv admin note: substantial text overlap with arXiv:2402.01775

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders.

Most applications of Artificial Intelligence (AI) are designed for a confined and specific task. However, there are many scenarios that call for a more general AI, capable of solving a wide array of tasks without being specifically designed for them. The term General-Purpose Artificial Intelligence Systems (GPAIS) has been defined to refer to these AI systems. To date, the possibility of an Artificial General Intelligence, powerful enough to perform any intellectual task as if it were human, or even improve it, has remained an aspiration, fiction, and considered a risk for our society. Whilst we might still be far from achieving that, GPAIS is a reality and sitting at the forefront of AI research. This work discusses existing definitions for GPAIS and proposes a new definition that allows for a gradual differentiation among types of GPAIS according to their properties and limitations. We distinguish between closed-world and open-world GPAIS, characterising their degree of autonomy and ability based on several factors such as adaptation to new tasks, competence in domains not intentionally trained for, ability to learn from few data, or proactive acknowledgment of their own limitations. We propose a taxonomy of approaches to realise GPAIS, describing research trends such as the use of AI techniques to improve another AI (AI-powered AI) or (single) foundation models. As a prime example, we delve into GenAI, aligning them with the concepts presented in the taxonomy. We explore multi-modality, which involves fusing various types of data sources to expand the capabilities of GPAIS. Through the proposed definition and taxonomy, our aim is to facilitate research collaboration across different areas that are tackling general purpose tasks, as they share many common aspects. Finally, we discuss the state of GPAIS, prospects, societal implications, and the need for regulation and governance.

By work of Jenkins and Strebel, given a Riemann surface X and a simple closed multi-curve $\alpha$ on it, there exists a unique quadratic differential q on X whose horizontal foliation is measure equivalent to $\alpha$. We study the distribution of the critical graphs of these differentials in the moduli space of metric ribbon graphs as the extremal length of the multi-curves goes to infinity, showing they equidistribute to the Kontsevich measure regardless of the initial choice of X., Comment: 33 pages, 3 figures. Comments welcome!

Trustworthy Artificial Intelligence (AI) is based on seven technical requirements sustained over three main pillars that should be met throughout the system's entire life cycle: it should be (1) lawful, (2) ethical, and (3) robust, both from a technical and a social perspective. However, attaining truly trustworthy AI concerns a wider vision that comprises the trustworthiness of all processes and actors that are part of the system's life cycle, and considers previous aspects from different lenses. A more holistic vision contemplates four essential axes: the global principles for ethical use and development of AI-based systems, a philosophical take on AI ethics, a risk-based approach to AI regulation, and the mentioned pillars and requirements. The seven requirements (human agency and oversight; robustness and safety; privacy and data governance; transparency; diversity, non-discrimination and fairness; societal and environmental wellbeing; and accountability) are analyzed from a triple perspective: What each requirement for trustworthy AI is, Why it is needed, and How each requirement can be implemented in practice. On the other hand, a practical approach to implement trustworthy AI systems allows defining the concept of responsibility of AI-based systems facing the law, through a given auditing process. Therefore, a responsible AI system is the resulting notion we introduce in this work, and a concept of utmost necessity that can be realized through auditing processes, subject to the challenges posed by the use of regulatory sandboxes. Our multidisciplinary vision of trustworthy AI culminates in a debate on the diverging views published lately about the future of AI. Our reflections in this matter conclude that regulation is a key for reaching a consensus among these views, and that trustworthy and responsible AI systems will be crucial for the present and future of our society., Comment: 30 pages, 5 figures, under second review

Evolutionary Computation algorithms have been used to solve optimization problems in relation with architectural, hyper-parameter or training configuration, forging the field known today as Neural Architecture Search. These algorithms have been combined with other techniques such as the pruning of Neural Networks, which reduces the complexity of the network, and the Transfer Learning, which lets the import of knowledge from another problem related to the one at hand. The usage of several criteria to evaluate the quality of the evolutionary proposals is also a common case, in which the performance and complexity of the network are the most used criteria. This work proposes MO-EvoPruneDeepTL, a multi-objective evolutionary pruning algorithm. MO-EvoPruneDeepTL uses Transfer Learning to adapt the last layers of Deep Neural Networks, by replacing them with sparse layers evolved by a genetic algorithm, which guides the evolution based in the performance, complexity and robustness of the network, being the robustness a great quality indicator for the evolved models. We carry out different experiments with several datasets to assess the benefits of our proposal. Results show that our proposal achieves promising results in all the objectives, and direct relation are presented among them. The experiments also show that the most influential neurons help us explain which parts of the input images are the most relevant for the prediction of the pruned neural network. Lastly, by virtue of the diversity within the Pareto front of pruning patterns produced by the proposal, it is shown that an ensemble of differently pruned models improves the overall performance and robustness of the trained networks., Comment: 28 pages, 11 figures

Explainable artificial intelligence is proposed to provide explanations for reasoning performed by an Artificial Intelligence. There is no consensus on how to evaluate the quality of these explanations, since even the definition of explanation itself is not clear in the literature. In particular, for the widely known Local Linear Explanations, there are qualitative proposals for the evaluation of explanations, although they suffer from theoretical inconsistencies. The case of image is even more problematic, where a visual explanation seems to explain a decision while detecting edges is what it really does. There are a large number of metrics in the literature specialized in quantitatively measuring different qualitative aspects so we should be able to develop metrics capable of measuring in a robust and correct way the desirable aspects of the explanations. In this paper, we propose a procedure called REVEL to evaluate different aspects concerning the quality of explanations with a theoretically coherent development. This procedure has several advances in the state of the art: it standardizes the concepts of explanation and develops a series of metrics not only to be able to compare between them but also to obtain absolute information regarding the explanation itself. The experiments have been carried out on image four datasets as benchmark where we show REVEL's descriptive and analytical power.

Airway segmentation is crucial for the examination, diagnosis, and prognosis of lung diseases, while its manual delineation is unduly burdensome. To alleviate this time-consuming and potentially subjective manual procedure, researchers have proposed methods to automatically segment airways from computerized tomography (CT) images. However, some small-sized airway branches (e.g., bronchus and terminal bronchioles) significantly aggravate the difficulty of automatic segmentation by machine learning models. In particular, the variance of voxel values and the severe data imbalance in airway branches make the computational module prone to discontinuous and false-negative predictions. especially for cohorts with different lung diseases. Attention mechanism has shown the capacity to segment complex structures, while fuzzy logic can reduce the uncertainty in feature representations. Therefore, the integration of deep attention networks and fuzzy theory, given by the fuzzy attention layer, should be an escalated solution for better generalization and robustness. This paper presents an efficient method for airway segmentation, comprising a novel fuzzy attention neural network and a comprehensive loss function to enhance the spatial continuity of airway segmentation. The deep fuzzy set is formulated by a set of voxels in the feature map and a learnable Gaussian membership function. Different from the existing attention mechanism, the proposed channel-specific fuzzy attention addresses the issue of heterogeneous features in different channels. Furthermore, a novel evaluation metric is proposed to assess both the continuity and completeness of airway structures. The efficiency, generalization and robustness of the proposed method have been proved by training on normal lung disease while testing on datasets of lung cancer, COVID-19 and pulmonary fibrosis., Comment: 12 pages, 5 figures, Submitted to IEEE TNNLS

Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to infinity, showing that they equidistribute to the Kontsevich measure on a corresponding moduli space of metric ribbon graphs. In particular, random subsurfaces look like random ribbon graphs, a law which does not depend on the initial choice of X. This result strengthens Mirzakhani's famous simple closed multi-geodesic counting theorems for hyperbolic surfaces., Comment: 48 pages, 8 figures. Comments welcome!

We prove an effective estimate with a power saving error term for the number of square-tiled surfaces in a connected component of a stratum of quadratic differentials whose vertical and horizontal foliations belong to prescribed mapping class group orbits and which have at most $L$ squares. This result strengthens asymptotic counting formulas in work of Delecroix, Goujard, Zograf, Zorich, and the author., Comment: 13 pages, 5 figures

The combination of convolutional and recurrent neural networks is a promising framework that allows the extraction of high-quality spatio-temporal features together with its temporal dependencies, which is key for time series prediction problems such as forecasting, classification or anomaly detection, amongst others. In this paper, the TSFEDL library is introduced. It compiles 20 state-of-the-art methods for both time series feature extraction and prediction, employing convolutional and recurrent deep neural networks for its use in several data mining tasks. The library is built upon a set of Tensorflow+Keras and PyTorch modules under the AGPLv3 license. The performance validation of the architectures included in this proposal confirms the usefulness of this Python package., Comment: 26 pages, 33 figures

There is a broad consensus on the importance of deep learning models in tasks involving complex data. Often, an adequate understanding of these models is required when focusing on the transparency of decisions in human-critical applications. Besides other explainability techniques, trustworthiness can be achieved by using counterfactuals, like the way a human becomes familiar with an unknown process: by understanding the hypothetical circumstances under which the output changes. In this work we argue that automated counterfactual generation should regard several aspects of the produced adversarial instances, not only their adversarial capability. To this end, we present a novel framework for the generation of counterfactual examples which formulates its goal as a multi-objective optimization problem balancing three different objectives: 1) plausibility, i.e., the likeliness of the counterfactual of being possible as per the distribution of the input data; 2) intensity of the changes to the original input; and 3) adversarial power, namely, the variability of the model's output induced by the counterfactual. The framework departs from a target model to be audited and uses a Generative Adversarial Network to model the distribution of input data, together with a multi-objective solver for the discovery of counterfactuals balancing among these objectives. The utility of the framework is showcased over six classification tasks comprising image and three-dimensional data. The experiments verify that the framework unveils counterfactuals that comply with intuition, increasing the trustworthiness of the user, and leading to further insights, such as the detection of bias and data misrepresentation., Comment: 52 pages, 14 figures, under review

Support vector machines (SVMs) are popular learning algorithms to deal with binary classification problems. They traditionally assume equal misclassification costs for each class; however, real-world problems may have an uneven class distribution. This article introduces EBCS-SVM: evolutionary bilevel cost-sensitive SVMs. EBCS-SVM handles imbalanced classification problems by simultaneously learning the support vectors and optimizing the SVM hyperparameters, which comprise the kernel parameter and misclassification costs. The resulting optimization problem is a bilevel problem, where the lower level determines the support vectors and the upper level the hyperparameters. This optimization problem is solved using an evolutionary algorithm (EA) at the upper level and sequential minimal optimization (SMO) at the lower level. These two methods work in a nested fashion, that is, the optimal support vectors help guide the search of the hyperparameters, and the lower level is initialized based on previous successful solutions. The proposed method is assessed using 70 datasets of imbalanced classification and compared with several state-of-the-art methods. The experimental results, supported by a Bayesian test, provided evidence of the effectiveness of EBCS-SVM when working with highly imbalanced datasets., Comment: Copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

In recent years, Deep Learning models have shown a great performance in complex optimization problems. They generally require large training datasets, which is a limitation in most practical cases. Transfer learning allows importing the first layers of a pre-trained architecture and connecting them to fully-connected layers to adapt them to a new problem. Consequently, the configuration of the these layers becomes crucial for the performance of the model. Unfortunately, the optimization of these models is usually a computationally demanding task. One strategy to optimize Deep Learning models is the pruning scheme. Pruning methods are focused on reducing the complexity of the network, assuming an expected performance penalty of the model once pruned. However, the pruning could potentially be used to improve the performance, using an optimization algorithm to identify and eventually remove unnecessary connections among neurons. This work proposes EvoPruneDeepTL, an evolutionary pruning model for Transfer Learning based Deep Neural Networks which replaces the last fully-connected layers with sparse layers optimized by a genetic algorithm. Depending on its solution encoding strategy, our proposed model can either perform optimized pruning or feature selection over the densely connected part of the neural network. We carry out different experiments with several datasets to assess the benefits of our proposal. Results show the contribution of EvoPruneDeepTL and feature selection to the overall computational efficiency of the network as a result of the optimization process. In particular, the accuracy is improved, reducing at the same time the number of active neurons in the final layers.

In her thesis, Mirzakhani showed that the number of simple closed geodesics of length $\leq L$ on a closed, connected, oriented hyperbolic surface $X$ of genus $g$ is asymptotic to $L^{6g-6}$ times a constant depending on the geometry of $X$. In this survey we give a detailed account of Mirzakhani's proof of this result aimed at non-experts. We draw inspiration from classic primitive lattice point counting results in homogeneous dynamics. The focus is on understanding how the general principles that drive the proof in the case of lattices also apply in the setting of hyperbolic surfaces., Comment: 34 pages, 17 figures

Federated learning is a machine learning paradigm that emerges as a solution to the privacy-preservation demands in artificial intelligence. As machine learning, federated learning is threatened by adversarial attacks against the integrity of the learning model and the privacy of data via a distributed approach to tackle local and global learning. This weak point is exacerbated by the inaccessibility of data in federated learning, which makes harder the protection against adversarial attacks and evidences the need to furtherance the research on defence methods to make federated learning a real solution for safeguarding data privacy. In this paper, we present an extensive review of the threats of federated learning, as well as as their corresponding countermeasures, attacks versus defences. This survey provides a taxonomy of adversarial attacks and a taxonomy of defence methods that depict a general picture of this vulnerability of federated learning and how to overcome it. Likewise, we expound guidelines for selecting the most adequate defence method according to the category of the adversarial attack. Besides, we carry out an extensive experimental study from which we draw further conclusions about the behaviour of attacks and defences and the guidelines for selecting the most adequate defence method according to the category of the adversarial attack. This study is finished leading to meditated learned lessons and challenges.

Removing the bias and variance of multicentre data has always been a challenge in large scale digital healthcare studies, which requires the ability to integrate clinical features extracted from data acquired by different scanners and protocols to improve stability and robustness. Previous studies have described various computational approaches to fuse single modality multicentre datasets. However, these surveys rarely focused on evaluation metrics and lacked a checklist for computational data harmonisation studies. In this systematic review, we summarise the computational data harmonisation approaches for multi-modality data in the digital healthcare field, including harmonisation strategies and evaluation metrics based on different theories. In addition, a comprehensive checklist that summarises common practices for data harmonisation studies is proposed to guide researchers to report their research findings more effectively. Last but not least, flowcharts presenting possible ways for methodology and metric selection are proposed and the limitations of different methods have been surveyed for future research., Comment: 54 pages, 14 figures, accepted by the Information Fusion journal

We show that Thurston's earthquake flow is strongly asymmetric in the sense that its normalizer is as small as possible inside the group of orbifold automorphisms of the bundle of measured geodesic laminations over moduli space. (At the level of Teichm\"uller space, such automorphisms correspond to homeomorphisms that are equivariant with respect to an automorphism of the mapping class group.) It follows that the earthquake flow does not extend to an $\mathrm{SL}(2,\mathbf{R})$-action of orbifold automorphisms and does not admit continuous renormalization self-symmetries. In particular, it is not conjugate to the Teichm\"uller horocycle flow via an orbifold map. This contrasts with a number of previous results, most notably Mirzakhani's theorem that the earthquake and Teichm\"uller horocycle flows are measurably conjugate., Comment: 17 pages, 2 figures. Expanded introduction, references, and some proofs

Available data in machine learning applications is becoming increasingly complex, due to higher dimensionality and difficult classes. There exists a wide variety of approaches to measuring complexity of labeled data, according to class overlap, separability or boundary shapes, as well as group morphology. Many techniques can transform the data in order to find better features, but few focus on specifically reducing data complexity. Most data transformation methods mainly treat the dimensionality aspect, leaving aside the available information within class labels which can be useful when classes are somehow complex. This paper proposes an autoencoder-based approach to complexity reduction, using class labels in order to inform the loss function about the adequacy of the generated variables. This leads to three different new feature learners, Scorer, Skaler and Slicer. They are based on Fisher's discriminant ratio, the Kullback-Leibler divergence and least-squares support vector machines, respectively. They can be applied as a preprocessing stage for a binary classification problem. A thorough experimentation across a collection of 27 datasets and a range of complexity and classification metrics shows that class-informed autoencoders perform better than 4 other popular unsupervised feature extraction techniques, especially when the final objective is using the data for a classification task., Comment: This paper has been accepted for publication by IEEE Transactions on Pattern Analysis and Machine Intelligence

We show that the Hausdorff dimension of any proper Teichm\"uller horocycle flow orbit closure on any $\mathrm{SL}{(2,\mathbf{R})}$-invariant subvariety of Abelian or quadratic differentials is bounded away from the dimension of the subvariety in terms of the polynomial mixing rate of the Teichm\"uller horocycle flow on the subvariety. The proof is based on abstract methods for measurable flows adapted from work of Bourgain and Katz on sparse ergodic theorems., Comment: 16 pages

Deep learning has outperformed other machine learning algorithms in a variety of tasks, and as a result, it is widely used. However, like other machine learning algorithms, deep learning, and convolutional neural networks (CNNs) in particular, perform worse when the data sets present label noise. Therefore, it is important to develop algorithms that help the training of deep networks and their generalization to noise-free test sets. In this paper, we propose a robust training strategy against label noise, called RAFNI, that can be used with any CNN. This algorithm filters and relabels instances of the training set based on the predictions and their probabilities made by the backbone neural network during the training process. That way, this algorithm improves the generalization ability of the CNN on its own. RAFNI consists of three mechanisms: two mechanisms that filter instances and one mechanism that relabels instances. In addition, it does not suppose that the noise rate is known nor does it need to be estimated. We evaluated our algorithm using different data sets of several sizes and characteristics. We also compared it with state-of-the-art models using the CIFAR10 and CIFAR100 benchmarks under different types and rates of label noise and found that RAFNI achieves better results in most cases., Comment: 24 pages, 5 figures

We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length $\leq L$ on an arbitrary closed, orientable, negatively curved surface. More generally, we prove estimates of the same kind for the number of free homotopy classes of filling closed curves of a given topological type on a closed, orientable surface whose geometric intersection number with respect to a given filling geodesic current is $\leq L$. The proofs rely on recent progress made on the study of the effective dynamics of the mapping class group on Teichm\"uller space and the space of closed curves of a closed, orientable surface, and introduce a novel method for addressing counting problems of mapping class group orbits that naturally yields power saving error terms. This method is also applied to study counting problems of mapping class group orbits of Teichm\"uller space with respect to Thurston's asymmetric metric., Comment: 34 pages, 6 figures. arXiv admin note: text overlap with arXiv:2104.01694

The research in anomaly detection lacks a unified definition of what represents an anomalous instance. Discrepancies in the nature itself of an anomaly lead to multiple paradigms of algorithms design and experimentation. Predictive maintenance is a special case, where the anomaly represents a failure that must be prevented. Related time-series research as outlier and novelty detection or time-series classification does not apply to the concept of an anomaly in this field, because they are not single points which have not been seen previously and may not be precisely annotated. Moreover, due to the lack of annotated anomalous data, many benchmarks are adapted from supervised scenarios. To address these issues, we generalise the concept of positive and negative instances to intervals to be able to evaluate unsupervised anomaly detection algorithms. We also preserve the imbalance scheme for evaluation through the proposal of the Preceding Window ROC, a generalisation for the calculation of ROC curves for time-series scenarios. We also adapt the mechanism from a established time-series anomaly detection benchmark to the proposed generalisations to reward early detection. Therefore, the proposal represents a flexible evaluation framework for the different scenarios. To show the usefulness of this definition, we include a case study of Big Data algorithms with a real-world time-series problem provided by the company ArcelorMittal, and compare the proposal with an evaluation method., Comment: 25 pages, 9 figures, 5 tables