On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia. Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions. We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization

Information Theory and Machine Learning

The recent successes of machine learning, especially regarding systems based on deep neural networks, have encouraged further research activities and raised a new set of challenges in understanding and designing complex machine learning algorithms. New applications require learning algorithms to be distributed, have transferable learning results, use computation resources efficiently, convergence quickly on online settings, have performance guarantees, satisfy fairness or privacy constraints, incorporate domain knowledge on model structures, etc. A new wave of developments in statistical learning theory and information theory has set out to address these challenges. This Special Issue, "Machine Learning and Information Theory", aims to collect recent results in this direction reflecting a diverse spectrum of visions and efforts to extend conventional theories and develop analysis tools for these complex machine learning systems

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Generative models: theory and applications

Given some samples from a data distribution, the central aim of generative modeling is to generate more samples from approximately the same distribution. This framework has recently seen an explosion in popularity, with impressive applications in image generation, language modeling and protein synthesis. The striking success of these methods motivates two key questions: under what conditions do generative models provide accurate approximations to the underlying data distribution, and can we extend the range of scenarios in which they may be applied? This thesis considers these questions in the context of two classes of generative models: diffusion models and importance weighted autoencoders. Diffusion models work by iteratively applying noise to the data distribution and then learning to remove this noise. They were originally introduced for real-valued data. However, for many potential applications our data is most naturally defined on another state space - perhaps a manifold, or a discrete space. We describe extensions of diffusion models to arbitrary state spaces, using generic Markov processes for noising, and show how such models can be effectively learned. We also provide a detailed study of a specific extension to discrete state spaces. Next, we investigate the approximation accuracy of diffusion models. We derive error bounds for flow matching - a generalization of diffusion models - and improve upon state-of-the-art bounds for diffusion models, using techniques inspired by stochastic localization. Importance weighted autoencoders (IWAEs) work by learning a latent variable representation of the data, using importance sampling in the evidence lower bound to get a tighter variational objective. IWAEs suffer from several limitations, including posterior variance underestimation, poor signal-to-noise ratio during training, and weight collapse in the importance sampling ratios. We propose an extension of the IWAE - the VR-IWAE - that addresses the first two of these three issues. We then provide a detailed theoretical study of the third, showing that it persists even for the VR-IWAE. We provide empirical demonstrations of these phenomena on a range of simulated and real-world data

White Paper 11: Artificial intelligence, robotics & data science

198 p. : 17 cmSIC white paper on Artificial Intelligence, Robotics and Data Science sketches a preliminary roadmap for addressing current R&D challenges associated with automated and autonomous machines. More than 50 research challenges investigated all over Spain by more than 150 experts within CSIC are presented in eight chapters. Chapter One introduces key concepts and tackles the issue of the integration of knowledge (representation), reasoning and learning in the design of artificial entities. Chapter Two analyses challenges associated with the development of theories –and supporting technologies– for modelling the behaviour of autonomous agents. Specifically, it pays attention to the interplay between elements at micro level (individual autonomous agent interactions) with the macro world (the properties we seek in large and complex societies). While Chapter Three discusses the variety of data science applications currently used in all fields of science, paying particular attention to Machine Learning (ML) techniques, Chapter Four presents current development in various areas of robotics. Chapter Five explores the challenges associated with computational cognitive models. Chapter Six pays attention to the ethical, legal, economic and social challenges coming alongside the development of smart systems. Chapter Seven engages with the problem of the environmental sustainability of deploying intelligent systems at large scale. Finally, Chapter Eight deals with the complexity of ensuring the security, safety, resilience and privacy-protection of smart systems against cyber threats.18 EXECUTIVE SUMMARY ARTIFICIAL INTELLIGENCE, ROBOTICS AND DATA SCIENCE Topic Coordinators Sara Degli Esposti ( IPP-CCHS, CSIC ) and Carles Sierra ( IIIA, CSIC ) 18 CHALLENGE 1 INTEGRATING KNOWLEDGE, REASONING AND LEARNING Challenge Coordinators Felip Manyà ( IIIA, CSIC ) and Adrià Colomé ( IRI, CSIC – UPC ) 38 CHALLENGE 2 MULTIAGENT SYSTEMS Challenge Coordinators N. Osman ( IIIA, CSIC ) and D. López ( IFS, CSIC ) 54 CHALLENGE 3 MACHINE LEARNING AND DATA SCIENCE Challenge Coordinators J. J. Ramasco Sukia ( IFISC ) and L. Lloret Iglesias ( IFCA, CSIC ) 80 CHALLENGE 4 INTELLIGENT ROBOTICS Topic Coordinators G. Alenyà ( IRI, CSIC – UPC ) and J. Villagra ( CAR, CSIC ) 100 CHALLENGE 5 COMPUTATIONAL COGNITIVE MODELS Challenge Coordinators M. D. del Castillo ( CAR, CSIC) and M. Schorlemmer ( IIIA, CSIC ) 120 CHALLENGE 6 ETHICAL, LEGAL, ECONOMIC, AND SOCIAL IMPLICATIONS Challenge Coordinators P. Noriega ( IIIA, CSIC ) and T. Ausín ( IFS, CSIC ) 142 CHALLENGE 7 LOW-POWER SUSTAINABLE HARDWARE FOR AI Challenge Coordinators T. Serrano ( IMSE-CNM, CSIC – US ) and A. Oyanguren ( IFIC, CSIC - UV ) 160 CHALLENGE 8 SMART CYBERSECURITY Challenge Coordinators D. Arroyo Guardeño ( ITEFI, CSIC ) and P. Brox Jiménez ( IMSE-CNM, CSIC – US )Peer reviewe