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 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 Learning Probabilistic Graphical Models in R written by David Bellot and published by Packt Publishing Ltd. This book was released on 2016-04-29 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Familiarize yourself with probabilistic graphical models through real-world problems and illustrative code examples in R About This Book Predict and use a probabilistic graphical models (PGM) as an expert system Comprehend how your computer can learn Bayesian modeling to solve real-world problems Know how to prepare data and feed the models by using the appropriate algorithms from the appropriate R package Who This Book Is For This book is for anyone who has to deal with lots of data and draw conclusions from it, especially when the data is noisy or uncertain. Data scientists, machine learning enthusiasts, engineers, and those who curious about the latest advances in machine learning will find PGM interesting. What You Will Learn Understand the concepts of PGM and which type of PGM to use for which problem Tune the model's parameters and explore new models automatically Understand the basic principles of Bayesian models, from simple to advanced Transform the old linear regression model into a powerful probabilistic model Use standard industry models but with the power of PGM Understand the advanced models used throughout today's industry See how to compute posterior distribution with exact and approximate inference algorithms In Detail Probabilistic graphical models (PGM, also known as graphical models) are a marriage between probability theory and graph theory. Generally, PGMs use a graph-based representation. Two branches of graphical representations of distributions are commonly used, namely Bayesian networks and Markov networks. R has many packages to implement graphical models. We'll start by showing you how to transform a classical statistical model into a modern PGM and then look at how to do exact inference in graphical models. Proceeding, we'll introduce you to many modern R packages that will help you to perform inference on the models. We will then run a Bayesian linear regression and you'll see the advantage of going probabilistic when you want to do prediction. Next, you'll master using R packages and implementing its techniques. Finally, you'll be presented with machine learning applications that have a direct impact in many fields. Here, we'll cover clustering and the discovery of hidden information in big data, as well as two important methods, PCA and ICA, to reduce the size of big problems. Style and approach This book gives you a detailed and step-by-step explanation of each mathematical concept, which will help you build and analyze your own machine learning models and apply them to real-world problems. The mathematics is kept simple and each formula is explained thoroughly.

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 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 Probabilistic Machine Learning written by Kevin P. Murphy and published by MIT Press. This book was released on 2023-08-15 with total page 1352 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced book for researchers and graduate students working in machine learning and statistics who want to learn about deep learning, Bayesian inference, generative models, and decision making under uncertainty. An advanced counterpart to Probabilistic Machine Learning: An Introduction, this high-level textbook provides researchers and graduate students detailed coverage of cutting-edge topics in machine learning, including deep generative modeling, graphical models, Bayesian inference, reinforcement learning, and causality. This volume puts deep learning into a larger statistical context and unifies approaches based on deep learning with ones based on probabilistic modeling and inference. With contributions from top scientists and domain experts from places such as Google, DeepMind, Amazon, Purdue University, NYU, and the University of Washington, this rigorous book is essential to understanding the vital issues in machine learning. Covers generation of high dimensional outputs, such as images, text, and graphs Discusses methods for discovering insights about data, based on latent variable models Considers training and testing under different distributions Explores how to use probabilistic models and inference for causal inference and decision making Features online Python code accompaniment

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 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 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 Handbook of Graphical Models written by Marloes Maathuis and published by CRC Press. This book was released on 2018-11-12 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference. While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Download or read book Probabilistic Graphical Models written by Ying Liu (Ph. D.) and published by . This book was released on 2014 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: In undirected graphical models, each node represents a random variable while the set of edges specifies the conditional independencies of the underlying distribution. When the random variables are jointly Gaussian, the models are called Gaussian graphical models (GGMs) or Gauss Markov random fields. In this thesis, we address several important problems in the study of GGMs. The first problem is to perform inference or sampling when the graph structure and model parameters are given. For inference in graphs with cycles, loopy belief propagation (LBP) is a purely distributed algorithm, but it gives inaccurate variance estimates in general and often diverges or has slow convergence. Previously, the hybrid feedback message passing (FMP) algorithm was developed to enhance the convergence and accuracy, where a special protocol is used among the nodes in a pseudo-FVS (an FVS, or feedback vertex set, is a set of nodes whose removal breaks all cycles) while standard LBP is run on the subgraph excluding the pseudo-FVS. In this thesis, we develop recursive FMP, a purely distributed extension of FMP where all nodes use the same integrated message-passing protocol. In addition, we introduce the subgraph perturbation sampling algorithm, which makes use of any pre-existing tractable inference algorithm for a subgraph by perturbing this algorithm so as to yield asymptotically exact samples for the intended distribution. We study the stationary version where a single fixed subgraph is used in all iterations, as well as the non-stationary version where tractable subgraphs are adaptively selected. The second problem is to perform model learning, i.e. to recover the underlying structure and model parameters from observations when the model is unknown. Families of graphical models that have both large modeling capacity and efficient inference algorithms are extremely useful. With the development of new inference algorithms for many new applications, it is important to study the families of models that are most suitable for these inference algorithms while having strong expressive power in the new applications. In particular, we study the family of GGMs with small FVSs and propose structure learning algorithms for two cases: 1) All nodes are observed, which is useful in modeling social or flight networks where the FVS nodes often correspond to a small number of high-degree nodes, or hubs, while the rest of the networks is modeled by a tree. 2) The FVS nodes are latent variables, where structure learning is equivalent to decomposing an inverse covariance matrix (exactly or approximately) into the sum of a tree-structured matrix and a low-rank matrix. We perform experiments using synthetic data as well as real data of flight delays to demonstrate the modeling capacity with FVSs of various sizes.

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 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 Semialgebraic Statistics and Latent Tree Models written by Piotr Zwiernik and published by CRC Press. This book was released on 2015-08-21 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints

Download or read book Structured Learning and Prediction in Computer Vision written by Sebastian Nowozin and published by Now Publishers Inc. This book was released on 2011 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured Learning and Prediction in Computer Vision introduces the reader to the most popular classes of structured models in computer vision.

Download or read book Latent Variable Modeling and Applications to Causality written by Maia Berkane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers refereed papers presented at the 1994 UCLA conference on "La tent Variable Modeling and Application to Causality. " The meeting was organized by the UCLA Interdivisional Program in Statistics with the purpose of bringing together a group of people who have done recent advanced work in this field. The papers in this volume are representative of a wide variety of disciplines in which the use of latent variable models is rapidly growing. The volume is divided into two broad sections. The first section covers Path Models and Causal Reasoning and the papers are innovations from contributors in disciplines not traditionally associated with behavioural sciences, (e. g. computer science with Judea Pearl and public health with James Robins). Also in this section are contri butions by Rod McDonald and Michael Sobel who have a more traditional approach to causal inference, generating from problems in behavioural sciences. The second section encompasses new approaches to questions of model selection with emphasis on factor analysis and time varying systems. Amemiya uses nonlinear factor analysis which has a higher order of complexity associated with the identifiability condi tions. Muthen studies longitudinal hierarchichal models with latent variables and treats the time vector as a variable rather than a level of hierarchy. Deleeuw extends exploratory factor analysis models by including time as a variable and allowing for discrete and ordi nal latent variables. Arminger looks at autoregressive structures and Bock treats factor analysis models for categorical data.

Download or read book Distributed and Accelerated Inference Algorithms for Probabilistic Graphical Models written by Arthur Uy Asuncion and published by . This book was released on 2011 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning graphical models from data is of fundamental importance in machine learning and statistics; however, this task is often computationally challenging due to the complexity of the models and the large scale of the data sets involved. This dissertation presents a variety of distributed and accelerated inference algorithms for probabilistic graphical models. The first part of this dissertation focuses on a class of directed latent variable models known as topic models. We introduce synchronous and asynchronous distributed algorithms for topic models which yield significant time and memory savings without sacrificing accuracy. We also investigate various approximate inference techniques for topic models, including collapsed Gibbs sampling, variational inference, and maximum a posteriori estimation and find that these methods learn models of similar accuracy as long as hyperparameters are optimized, giving us the freedom to utilize the most computationally efficient algorithm. The second part of this dissertation focuses on accelerated parameter estimation techniques for undirected models such as Boltzmann machines and exponential random graph models. We investigate an efficient blocked contrastive divergence approach that is based on the composite likelihood framework. We also present a particle filtering approach for approximate maximum likelihood estimation that is able to outperform previously proposed estimation algorithms.