Download or read book Global Variational Learning for Graphical Models with Latent Variables written by Ahmed M. Abdelatty and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Graphical Models have been used intensively for developing Machine Learning applications including Computer Vision, Natural Language processing, Collaborative Filtering, and Bioinformatics. Moreover, Graphical Models with latent variables are very powerful tools for modeling uncertainty, since latent variables can be used to represent unobserved factors, and they also can be used to model the correlations between the observed variables. However, global learning of Latent Variable Models (LVMs) is NP-hard in general, and the state-of-the-art algorithm for learning them such as Expectation Maximization algorithm can get stuck in local optimum. In this thesis, we address the problem of global variational learning for LVMs. More precisely, we propose a convex variational approximation for Maximum Likelihood Learning and apply Frank-Wolfe algorithm to solve it. We also investigate the use of the Global Optimization Algorithm (GOP) for Bayesian Learning, and we demonstrate that it converges to the global optimum.

Download or read book Learning in Graphical Models written by M.I. Jordan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, a number of different research communities within the computational sciences have studied learning in networks, starting from a number of different points of view. There has been substantial progress in these different communities and surprising convergence has developed between the formalisms. The awareness of this convergence and the growing interest of researchers in understanding the essential unity of the subject underlies the current volume. Two research communities which have used graphical or network formalisms to particular advantage are the belief network community and the neural network community. Belief networks arose within computer science and statistics and were developed with an emphasis on prior knowledge and exact probabilistic calculations. Neural networks arose within electrical engineering, physics and neuroscience and have emphasised pattern recognition and systems modelling problems. This volume draws together researchers from these two communities and presents both kinds of networks as instances of a general unified graphical formalism. The book focuses on probabilistic methods for learning and inference in graphical models, algorithm analysis and design, theory and applications. Exact methods, sampling methods and variational methods are discussed in detail. Audience: A wide cross-section of computationally oriented researchers, including computer scientists, statisticians, electrical engineers, physicists and neuroscientists.

Download or read book Variational Methods for Machine Learning with Applications to Deep Networks written by Lucas Pinheiro Cinelli and published by Springer Nature. This book was released on 2021-05-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a straightforward look at the concepts, algorithms and advantages of Bayesian Deep Learning and Deep Generative Models. Starting from the model-based approach to Machine Learning, the authors motivate Probabilistic Graphical Models and show how Bayesian inference naturally lends itself to this framework. The authors present detailed explanations of the main modern algorithms on variational approximations for Bayesian inference in neural networks. Each algorithm of this selected set develops a distinct aspect of the theory. The book builds from the ground-up well-known deep generative models, such as Variational Autoencoder and subsequent theoretical developments. By also exposing the main issues of the algorithms together with different methods to mitigate such issues, the book supplies the necessary knowledge on generative models for the reader to handle a wide range of data types: sequential or not, continuous or not, labelled or not. The book is self-contained, promptly covering all necessary theory so that the reader does not have to search for additional information elsewhere. Offers a concise self-contained resource, covering the basic concepts to the algorithms for Bayesian Deep Learning; Presents Statistical Inference concepts, offering a set of elucidative examples, practical aspects, and pseudo-codes; Every chapter includes hands-on examples and exercises and a website features lecture slides, additional examples, and other support material.

Download or read book Provable Algorithms for Learning and Variational Inference in Undirected Graphical Models written by Frederic Koehler and published by . This book was released on 2021 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical models are a general-purpose tool for modeling complex distributions in a way which facilitates probabilistic reasoning, with numerous applications across machine learning and the sciences. This thesis deals with algorithmic and statistical problems of learning a high-dimensional graphical model from samples, and related problems of performing inference on a known model, both areas of research which have been the subject of continued interest over the years. Our main contributions are the first computationally efficient algorithms for provably (1) learning a (possibly ill-conditioned) walk-summable Gaussian Graphical Model from samples, (2) learning a Restricted Boltzmann Machine (or other latent variable Ising model) from data, and (3) performing naive mean-field variational inference on an Ising model in the optimal density regime. These different problems illustrate a set of key principles, such as the diverse algorithmic applications of "pinning" variables in graphical models. We also show in some cases that these results are nearly optimal due to matching computational/cryptographic hardness results

Download or read book Learning and Inference in Latent Variable Graphical Models written by Wei Ping and published by . This book was released on 2016 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic graphical models such as Markov random fields provide a powerful framework and tools for machine learning, especially for structured output learning. Latent variables naturally exist in many applications of these models; they may arise from partially labeled data, or be introduced to enrich model flexibility. However, the presence of latent variables presents challenges for learning and inference.For example, the standard approach of using maximum a posteriori (MAP) prediction is complicated by the fact that, in latent variable models (LVMs), we typically want to first marginalize out the latent variables, leading to an inference task called marginal MAP. Unfortunately, marginal MAP prediction can be NP-hard even on relatively simple models such as trees, and few methods have been developed in the literature. This thesis presents a class of variational bounds for marginal MAP that generalizes the popular dual-decomposition method for MAP inference, and enables an efficient block coordinate descent algorithm to solve the corresponding optimization. Similarly, when learning LVMs for structured prediction, it is critically important to maintain the effect of uncertainty over latent variables by marginalization. We propose the marginal structured SVM, which uses marginal MAP inference to properly handle that uncertainty inside the framework of max-margin learning.We then turn our attention to an important subclass of latent variable models, restricted Boltzmann machines (RBMs). RBMs are two-layer latent variable models that are widely used to capture complex distributions of observed data, including as building block for deep probabilistic models. One practical problem in RBMs is model selection: we need to determine the hidden (latent) layer size before performing learning. We propose an infinite RBM model and apply the Frank-Wolfe algorithm to solve the resulting learning problem. The resulting algorithm can be interpreted as inserting a hidden variable into a RBM model at each iteration, to easily and efficiently perform model selection during learning. We also study the role of approximate inference in RBMs and conditional RBMs. In particular, there is a common assumption that belief propagation methods do not work well on RBM-based models, especially for learning. In contrast, we demonstrate that for conditional models and structured prediction, learning RBM-based models with belief propagation and its variants can provide much better results than the state-of-the-art contrastive divergence methods.

Download or read book Latent Variable Models and Factor Analysis written by David J. Bartholomew and published by Wiley. This book was released on 1999-08-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hitherto latent variable modelling has hovered on the fringes of the statistical mainstream but if the purpose of statistics is to deal with real problems, there is every reason for it to move closer to centre stage. In the social sciences especially, latent variables are common and if they are to be handled in a truly scientific manner, statistical theory must be developed to include them. This book aims to show how that should be done. This second edition is a complete re-working of the book of the same name which appeared in the Griffin’s Statistical Monographs in 1987. Since then there has been a surge of interest in latent variable methods which has necessitated a radical revision of the material but the prime object of the book remains the same. It provides a unified and coherent treatment of the field from a statistical perspective. This is achieved by setting up a sufficiently general framework to enable the derivation of the commonly used models. The subsequent analysis is then done wholly within the realm of probability calculus and the theory of statistical inference. Numerical examples are provided as well as the software to carry them out ( where this is not otherwise available). Additional data sets are provided in some cases so that the reader can aquire a wider experience of analysis and interpretation.

Download or read book An Introduction to Variational Autoencoders written by Diederik P. Kingma and published by . This book was released on 2019-11-12 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Variational Autoencoders provides a quick summary for the of a topic that has become an important tool in modern-day deep learning techniques.

Download or read book Graphical Models for Machine Learning and Digital Communication written by Brendan J. Frey and published by MIT Press. This book was released on 1998 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content Description. #Includes bibliographical references and index.

Download or read book Graphical Models Exponential Families and Variational Inference written by Martin J. Wainwright and published by Now Publishers Inc. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.

Download or read book Learning Directed Graphical Models with Latent Variables written by Basil N. Saeed and published by . This book was released on 2020 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of learning directed graphical models with latent variables, represented by directed maximal ancestral graphs, from a conditional independence oracle. We show that given a set of separation statements from some directed maximal ancestral graph G* = (V*,E*), we can map posets with ground set V* to minimal IMAPs of G* such that the sparsest of these minimal IMAPs is Markov equivalent to G*. We give a diagrammatic interpretation of these minimal IMAPs in terms of the Hasse diagram of the poset of posets. Namely, the Hasse diagram of these minimal IMAPs corresponds to the Hasse diagram of the poset of posets after identifying posets that map to the same minimal IMAP. We show that moving between these minimal IMAPs using legitimate mark changes corresponds to covering relations in the poset obtained after identification. Finally, we conjecture that a greedy search to minimize sparsity over this contracted space by moving between minimal IMAPs using legitimate mark changes converges to G*.

Download or read book Probabilistic Graphical Models written by Daphne Koller and published by MIT Press. This book was released on 2009-07-31 with total page 1270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions. Most tasks require a person or an automated system to reason—to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Download or read book Learning Bayesian Networks written by Richard E. Neapolitan and published by Prentice Hall. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first edition book, methods are discussed for doing inference in Bayesian networks and inference diagrams. Hundreds of examples and problems allow readers to grasp the information. Some of the topics discussed include Pearl's message passing algorithm, Parameter Learning: 2 Alternatives, Parameter Learning r Alternatives, Bayesian Structure Learning, and Constraint-Based Learning. For expert systems developers and decision theorists.

Download or read book Statistical Factor Analysis and Related Methods written by Alexander T. Basilevsky and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Factor Analysis and Related Methods Theory andApplications In bridging the gap between the mathematical andstatistical theory of factor analysis, this new work represents thefirst unified treatment of the theory and practice of factoranalysis and latent variable models. It focuses on such areasas: * The classical principal components model and sample-populationinference * Several extensions and modifications of principal components,including Q and three-mode analysis and principal components in thecomplex domain * Maximum likelihood and weighted factor models, factoridentification, factor rotation, and the estimation of factorscores * The use of factor models in conjunction with various types ofdata including time series, spatial data, rank orders, and nominalvariable * Applications of factor models to the estimation of functionalforms and to least squares of regression estimators

Download or read book Variational Bayesian Learning Theory written by Shinichi Nakajima and published by Cambridge University Press. This book was released on 2019-07-11 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of variational Bayesian learning summarizes recent developments and suggests practical applications.

Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Download or read book Bayesian Statistics 7 written by J. M. Bernardo and published by Oxford University Press. This book was released on 2003-07-03 with total page 1114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 7th Valencia International Meeting on Bayesian Statistics. This conference is held every four years and provides the main forum for researchers in the area of Bayesian statistics to come together to present and discuss frontier developments in the field.