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 The Variational Bayes Method in Signal Processing written by Václav Šmídl and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treating VB approximation in signal processing, this monograph is for academic and industrial research groups in signal processing, data analysis, machine learning and identification. It reviews distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts.

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 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 Machine learning using approximate inference written by Christian Andersson Naesseth and published by Linköping University Electronic Press. This book was released on 2018-11-27 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models. There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them. First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.

Download or read book Variational Bayesian Learning and Its Applications written by Hui Zhao and published by . This book was released on 2013 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is devoted to studying a fast and analytic approximation method, called the variational Bayesian (VB) method, and aims to give insight into its general applicability and usefulness, and explore its applications to various real-world problems. This work has three main foci: 1) The general applicability and properties; 2) Diagnostics for VB approximations; 3) Variational applications. Generally, the variational inference has been developed in the context of the exponential family, which is open to further development. First, it usually consider the cases in the context of the conjugate exponential family. Second, the variational inferences are developed only with respect to natural parameters, which are often not the parameters of immediate interest. Moreover, the full factorization, which assumes all terms to be independent of one another, is the most commonly used scheme in the most of the variational applications. We show that VB inferences can be extended to a more general situation. We propose a special parameterization for a parametric family, and also propose a factorization scheme with a more general dependency structure than is traditional in VB. Based on these new frameworks, we develop a variational formalism, in which VB has a fast implementation, and not be limited to the conjugate exponential setting. We also investigate its local convergence property, the effects of choosing different priors, and the effects of choosing different factorization scheme. The essence of the VB method relies on making simplifying assumptions about the posterior dependence of a problem. By definition, the general posterior dependence structure is distorted. In addition, in the various applications, we observe that the posterior variances are often underestimated. We aim to develop diagnostics test to assess VB approximations, and these methods are expected to be quick and easy to use, and to require no sophisticated tuning expertise. We propose three methods to compute the actual posterior covariance matrix by only using the knowledge obtained from VB approximations: 1) To look at the joint posterior distribution and attempt to find an optimal affine transformation that links the VB and true posteriors; 2) Based on a marginal posterior density approximation to work in specific low dimensional directions to estimate true posterior variances and correlations; 3) Based on a stepwise conditional approach, to construct and solve a set of system of equations that lead to estimates of the true posterior variances and correlations. A key computation in the above methods is to calculate a uni-variate marginal or conditional variance. We propose a novel way, called the VB Adjusted Independent Metropolis-Hastings (VBAIMH) method, to compute these quantities. It uses an independent Metropolis-Hastings (IMH) algorithm with proposal distributions configured by VB approximations. The variance of the target distribution is obtained by monitoring the acceptance rate of the generated chain. One major question associated with the VB method is how well the approximations can work. We particularly study the mean structure approximations, and show how it is possible using VB approximations to approach model selection tasks such as determining the dimensionality of a model, or variable selection. We also consider the variational application in Bayesian nonparametric modeling, especially for the Dirichlet process (DP). The posterior inference for DP has been extensively studied in the context of MCMC methods. This work presents a a full variational solution for DP with non-conjugate settings. Our solution uses a truncated stick-breaking representation. We propose an empirical method to determine the number of distinct components in a finite dimensional DP. The posterior predictive distribution for DP is often not available in a closed form. We show how to use the variational techniques to approximate this quantity. As a concrete application study, we work through the VB method on regime-switching lognormal models and present solutions to quantify both the uncertainty in the parameters and model specification. Through a series numerical comparison studies with likelihood based methods and MCMC methods on the simulated and real data sets, we show that the VB method can recover exactly the model structure, gives the reasonable point estimates, and is very computationally efficient.

Download or read book Algorithmic Learning Theory written by Sanjay Jain and published by Springer Science & Business Media. This book was released on 2005-09-26 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th International Conference on Algorithmic Learning Theory, ALT 2005, held in Singapore in October 2005. The 30 revised full papers presented together with 5 invited papers and an introduction by the editors were carefully reviewed and selected from 98 submissions. The papers are organized in topical sections on kernel-based learning, bayesian and statistical models, PAC-learning, query-learning, inductive inference, language learning, learning and logic, learning from expert advice, online learning, defensive forecasting, and teaching.

Download or read book Advanced Lectures on Machine Learning written by Olivier Bousquet and published by Springer. This book was released on 2011-03-22 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in Tübingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.

Download or read book Bayesian Learning written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2023-07-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Bayesian Learning In the field of statistics, an expectation-maximization (EM) algorithm is an iterative approach to discover (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. EM algorithms are also known as maximum likelihood or maximum a posteriori (MAP) estimations. The expectation (E) step of the EM iteration creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and the maximization (M) step of the EM iteration computes parameters with the goal of maximizing the expected log-likelihood found on the expectation step. These two steps are performed in alternating fashion throughout the iteration. These parameter-estimates are then utilized in the subsequent E phase, which serves the purpose of determining the distribution of the latent variables. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Expectation-maximization algorithm Chapter 2: Likelihood function Chapter 3: Maximum likelihood estimation Chapter 4: Logistic regression Chapter 5: Exponential family Chapter 6: Fisher information Chapter 7: Generalized linear model Chapter 8: Mixture model Chapter 9: Variational Bayesian methods Chapter 10: EM algorithm and GMM model (II) Answering the public top questions about bayesian learning. (III) Real world examples for the usage of bayesian learning in many fields. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of bayesian learning. What is Artificial Intelligence Series The artificial intelligence book series provides comprehensive coverage in over 200 topics. Each ebook covers a specific Artificial Intelligence topic in depth, written by experts in the field. The series aims to give readers a thorough understanding of the concepts, techniques, history and applications of artificial intelligence. Topics covered include machine learning, deep learning, neural networks, computer vision, natural language processing, robotics, ethics and more. The ebooks are written for professionals, students, and anyone interested in learning about the latest developments in this rapidly advancing field. The artificial intelligence book series provides an in-depth yet accessible exploration, from the fundamental concepts to the state-of-the-art research. With over 200 volumes, readers gain a thorough grounding in all aspects of Artificial Intelligence. The ebooks are designed to build knowledge systematically, with later volumes building on the foundations laid by earlier ones. This comprehensive series is an indispensable resource for anyone seeking to develop expertise in artificial intelligence.

Download or read book Information Theory Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Download or read book Bayesian Nonparametrics written by Nils Lid Hjort and published by Cambridge University Press. This book was released on 2010-04-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.

Download or read book Machine Learning and Information Processing written by Debabala Swain and published by Springer Nature. This book was released on 2021-04-02 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes selected papers from the 2nd International Conference on Machine Learning and Information Processing (ICMLIP 2020), held at Vardhaman College of Engineering, Jawaharlal Nehru Technological University (JNTU), Hyderabad, India, from November 28 to 29, 2020. It presents the latest developments and technical solutions in the areas of advanced computing and data sciences, covering machine learning, artificial intelligence, human–computer interaction, IoT, deep learning, image processing and pattern recognition, and signal and speech processing.

Download or read book Active Inference written by Thomas Parr and published by MIT Press. This book was released on 2022-03-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive treatment of active inference, an integrative perspective on brain, cognition, and behavior used across multiple disciplines. Active inference is a way of understanding sentient behavior—a theory that characterizes perception, planning, and action in terms of probabilistic inference. Developed by theoretical neuroscientist Karl Friston over years of groundbreaking research, active inference provides an integrated perspective on brain, cognition, and behavior that is increasingly used across multiple disciplines including neuroscience, psychology, and philosophy. Active inference puts the action into perception. This book offers the first comprehensive treatment of active inference, covering theory, applications, and cognitive domains. Active inference is a “first principles” approach to understanding behavior and the brain, framed in terms of a single imperative to minimize free energy. The book emphasizes the implications of the free energy principle for understanding how the brain works. It first introduces active inference both conceptually and formally, contextualizing it within current theories of cognition. It then provides specific examples of computational models that use active inference to explain such cognitive phenomena as perception, attention, memory, and planning.

Download or read book Computational Bayesian Statistics written by M. Antónia Amaral Turkman and published by Cambridge University Press. This book was released on 2019-02-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This integrated introduction to fundamentals, computation, and software is your key to understanding and using advanced Bayesian methods.

Download or read book Advanced Mean Field Methods written by Manfred Opper and published by MIT Press. This book was released on 2001 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Download or read book Bayesian Time Series Models written by David Barber and published by Cambridge University Press. This book was released on 2011-08-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.

Download or read book Bayesian Analysis in Natural Language Processing written by Shay Cohen and published by Springer Nature. This book was released on 2022-11-10 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural language processing (NLP) went through a profound transformation in the mid-1980s when it shifted to make heavy use of corpora and data-driven techniques to analyze language. Since then, the use of statistical techniques in NLP has evolved in several ways. One such example of evolution took place in the late 1990s or early 2000s, when full-fledged Bayesian machinery was introduced to NLP. This Bayesian approach to NLP has come to accommodate for various shortcomings in the frequentist approach and to enrich it, especially in the unsupervised setting, where statistical learning is done without target prediction examples. We cover the methods and algorithms that are needed to fluently read Bayesian learning papers in NLP and to do research in the area. These methods and algorithms are partially borrowed from both machine learning and statistics and are partially developed "in-house" in NLP. We cover inference techniques such as Markov chain Monte Carlo sampling and variational inference, Bayesian estimation, and nonparametric modeling. We also cover fundamental concepts in Bayesian statistics such as prior distributions, conjugacy, and generative modeling. Finally, we cover some of the fundamental modeling techniques in NLP, such as grammar modeling and their use with Bayesian analysis.