Author: Christian Andersson Naesseth
Publisher: Linköping University Electronic Press
ISBN: 9176851613
Category :
Languages : en
Pages : 39
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Book Description
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.
Author: Marcel Andre Hirt
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Olivier Bousquet
Publisher: Springer
ISBN: 3540286500
Category : Computers
Languages : en
Pages : 249
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Book Description
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.
Author: David J. C. MacKay
Publisher: Cambridge University Press
ISBN: 9780521642989
Category : Computers
Languages : en
Pages : 694
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Book Description
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.
Author: Pradeep Ravikumar
Publisher:
ISBN:
Category : Graphical modeling (Statistics)
Languages : en
Pages : 139
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Book Description
Abstract: "Markov random fields (MRFs), or undirected graphical models, are graphical representations of probability distributions. Each graph represents a family of distributions -- the nodes of the graph represent random variables, the edges encode independence assumptions, and weights over the edges and cliques specify a particular member of the family. There are three main classes of tasks within this framework: the first is to perform inference, given the graph structure and parameters and (clique) feature functions; the second is to estimate the graph structure and parameters from data, given the feature functions; the third is to estimate the feature functions themselves from data. Key inference subtasks include estimating the normalization constant (also called the partition function), event probability estimation, computing rigorous upper and lower bounds (interval guarantees), inference given only moment constraints, and computing the most probable configuration. The thesis addresses all of the above tasks and subtasks."
Author: Julian Hippolyt Ritter
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Guy Van den Broeck
Publisher: MIT Press
ISBN: 0262542595
Category : Computers
Languages : en
Pages : 455
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Book Description
Recent advances in the area of lifted inference, which exploits the structure inherent in relational probabilistic models. Statistical relational AI (StaRAI) studies the integration of reasoning under uncertainty with reasoning about individuals and relations. The representations used are often called relational probabilistic models. Lifted inference is about how to exploit the structure inherent in relational probabilistic models, either in the way they are expressed or by extracting structure from observations. This book covers recent significant advances in the area of lifted inference, providing a unifying introduction to this very active field. After providing necessary background on probabilistic graphical models, relational probabilistic models, and learning inside these models, the book turns to lifted inference, first covering exact inference and then approximate inference. In addition, the book considers the theory of liftability and acting in relational domains, which allows the connection of learning and reasoning in relational domains.
Author: David Barber
Publisher: Cambridge University Press
ISBN: 0521518148
Category : Computers
Languages : en
Pages : 739
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Book Description
A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.
Author: John Winn
Publisher: CRC Press
ISBN: 1498756824
Category : Business & Economics
Languages : en
Pages : 469
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Book Description
Today, machine learning is being applied to a growing variety of problems in a bewildering variety of domains. A fundamental challenge when using machine learning is connecting the abstract mathematics of a machine learning technique to a concrete, real world problem. This book tackles this challenge through model-based machine learning which focuses on understanding the assumptions encoded in a machine learning system and their corresponding impact on the behaviour of the system. The key ideas of model-based machine learning are introduced through a series of case studies involving real-world applications. Case studies play a central role because it is only in the context of applications that it makes sense to discuss modelling assumptions. Each chapter introduces one case study and works through step-by-step to solve it using a model-based approach. The aim is not just to explain machine learning methods, but also showcase how to create, debug, and evolve them to solve a problem. Features: Explores the assumptions being made by machine learning systems and the effect these assumptions have when the system is applied to concrete problems. Explains machine learning concepts as they arise in real-world case studies. Shows how to diagnose, understand and address problems with machine learning systems. Full source code available, allowing models and results to be reproduced and explored. Includes optional deep-dive sections with more mathematical details on inference algorithms for the interested reader.
Author: Sergios Theodoridis
Publisher: Academic Press
ISBN: 0128188049
Category : Technology & Engineering
Languages : en
Pages : 1162
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Book Description
Machine Learning: A Bayesian and Optimization Perspective, 2nd edition, gives a unified perspective on machine learning by covering both pillars of supervised learning, namely regression and classification. The book starts with the basics, including mean square, least squares and maximum likelihood methods, ridge regression, Bayesian decision theory classification, logistic regression, and decision trees. It then progresses to more recent techniques, covering sparse modelling methods, learning in reproducing kernel Hilbert spaces and support vector machines, Bayesian inference with a focus on the EM algorithm and its approximate inference variational versions, Monte Carlo methods, probabilistic graphical models focusing on Bayesian networks, hidden Markov models and particle filtering. Dimensionality reduction and latent variables modelling are also considered in depth. This palette of techniques concludes with an extended chapter on neural networks and deep learning architectures. The book also covers the fundamentals of statistical parameter estimation, Wiener and Kalman filtering, convexity and convex optimization, including a chapter on stochastic approximation and the gradient descent family of algorithms, presenting related online learning techniques as well as concepts and algorithmic versions for distributed optimization. Focusing on the physical reasoning behind the mathematics, without sacrificing rigor, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. Most of the chapters include typical case studies and computer exercises, both in MATLAB and Python. The chapters are written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as courses on sparse modeling, deep learning, and probabilistic graphical models. New to this edition: - Complete re-write of the chapter on Neural Networks and Deep Learning to reflect the latest advances since the 1st edition. The chapter, starting from the basic perceptron and feed-forward neural networks concepts, now presents an in depth treatment of deep networks, including recent optimization algorithms, batch normalization, regularization techniques such as the dropout method, convolutional neural networks, recurrent neural networks, attention mechanisms, adversarial examples and training, capsule networks and generative architectures, such as restricted Boltzman machines (RBMs), variational autoencoders and generative adversarial networks (GANs). - Expanded treatment of Bayesian learning to include nonparametric Bayesian methods, with a focus on the Chinese restaurant and the Indian buffet processes. - Presents the physical reasoning, mathematical modeling and algorithmic implementation of each method - Updates on the latest trends, including sparsity, convex analysis and optimization, online distributed algorithms, learning in RKH spaces, Bayesian inference, graphical and hidden Markov models, particle filtering, deep learning, dictionary learning and latent variables modeling - Provides case studies on a variety of topics, including protein folding prediction, optical character recognition, text authorship identification, fMRI data analysis, change point detection, hyperspectral image unmixing, target localization, and more
