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Author: University of Regina. Department of Computer Science
Publisher: Regina : Department of Computer Science, University of Regina
ISBN: 9780773102934
Category :
Languages : en
Pages : 15
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Book Description
Author: University of Regina. Department of Computer Science
Publisher: Regina : Department of Computer Science, University of Regina
ISBN: 9780773102934
Category :
Languages : en
Pages : 15
Get Book Here
Book Description
Author: Daphne Koller
Publisher: MIT Press
ISBN: 0262258358
Category : Computers
Languages : en
Pages : 1270
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Book Description
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.
Author: Marco Scutari
Publisher: CRC Press
ISBN: 1000410382
Category : Computers
Languages : en
Pages : 275
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Book Description
Explains the material step-by-step starting from meaningful examples Steps detailed with R code in the spirit of reproducible research Real world data analyses from a Science paper reproduced and explained in detail Examples span a variety of fields across social and life sciences Overview of available software in and outside R
Author: Judea Pearl
Publisher: John Wiley & Sons
ISBN: 1119186862
Category : Mathematics
Languages : en
Pages : 162
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Book Description
CAUSAL INFERENCE IN STATISTICS A Primer Causality is central to the understanding and use of data. Without an understanding of cause–effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data. Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest. This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.
Author: Ramon Sangüesa i Solé
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Author: Finn V. Jensen
Publisher: Springer
ISBN: 9780387915029
Category : Mathematics
Languages : en
Pages : 178
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Book Description
Disk contains: Tool for building Bayesian networks -- Library of examples -- Library of proposed solutions to some exercises.
Author: P.E. Pfeiffer
Publisher: Springer Science & Business Media
ISBN: 1461263352
Category : Science
Languages : en
Pages : 160
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Book Description
It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.
Author: Luis Enrique Sucar
Publisher: Springer Nature
ISBN: 3030619435
Category : Computers
Languages : en
Pages : 370
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Book Description
This fully updated new edition of a uniquely accessible textbook/reference provides a general introduction to probabilistic graphical models (PGMs) from an engineering perspective. It features new material on partially observable Markov decision processes, causal graphical models, causal discovery and deep learning, as well as an even greater number of exercises; it also incorporates a software library for several graphical models in Python. The book covers the fundamentals for each of the main classes of PGMs, including representation, inference and learning principles, and reviews real-world applications for each type of model. These applications are drawn from a broad range of disciplines, highlighting the many uses of Bayesian classifiers, hidden Markov models, Bayesian networks, dynamic and temporal Bayesian networks, Markov random fields, influence diagrams, and Markov decision processes. Topics and features: Presents a unified framework encompassing all of the main classes of PGMs Explores the fundamental aspects of representation, inference and learning for each technique Examines new material on partially observable Markov decision processes, and graphical models Includes a new chapter introducing deep neural networks and their relation with probabilistic graphical models Covers multidimensional Bayesian classifiers, relational graphical models, and causal models Provides substantial chapter-ending exercises, suggestions for further reading, and ideas for research or programming projects Describes classifiers such as Gaussian Naive Bayes, Circular Chain Classifiers, and Hierarchical Classifiers with Bayesian Networks Outlines the practical application of the different techniques Suggests possible course outlines for instructors This classroom-tested work is suitable as a textbook for an advanced undergraduate or a graduate course in probabilistic graphical models for students of computer science, engineering, and physics. Professionals wishing to apply probabilistic graphical models in their own field, or interested in the basis of these techniques, will also find the book to be an invaluable reference. Dr. Luis Enrique Sucar is a Senior Research Scientist at the National Institute for Astrophysics, Optics and Electronics (INAOE), Puebla, Mexico. He received the National Science Prize en 2016.
Author: Tianhong Sheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Conditional independence is one of the most fundamental mechanisms underlying many statistical methods, such as probabilistic graphical models, causal discovery, feature selection, dimensionality reduction, and Bayesian network learning. The three topics in this thesis are all related to exploring, testing, and validating conditional independence. On the theoretical side, we study the properties of different types measures of conditional independence and the connections between the kernel-based measures and distance-based measures. On the methodology side, we develop a new type of probabilistic graphical models based on conditional independence under a skewed Gaussian distribution assumption. Furthermore, inspired by the tuning parameter selection scheme in the graphical models, we develop a new model selection scheme called "omnibus cross-validation" which is a general cross-validation scheme that can be applied to a wide range of variable selection problems. In Chapter 3, we explore the connection between conditional independence measures induced by distances on a metric space and reproducing kernels associated with a reproducing kernel Hilbert space (RKHS). For certain distance and kernel pairs, we show the distance-based conditional independence measures to be equivalent to that of kernel-based measures. On the other hand, we also show that some popular kernel conditional independence measures in machine learning, which are based on the Hilbert-Schmidt norm of a certain cross-conditional covariance operator, do not have a simple distance representation, except in some limited cases. This chapter shows that the distance and kernel measures of conditional independence are not quite equivalent unlike in the case of joint independence as shown by Sejdinovic et al. (2013). In Chapter 4, we introduce a skewed Gaussian graphical model as an extension to the Gaussian graphical model. One of the appealing properties of the Gaussian distribution is that conditional independence can be fully characterized by the sparseness in the precision matrix. The skewed Gaussian distribution adds a shape parameter to the Gaussian distribution to take into account possible skewness in the data; thus it is more flexible than the Gaussian model. Nevertheless, the appealing property of the Gaussian distribution is retained to a large degree: the conditional independence is still characterized by the sparseness in the parameters, which now include a shape parameter in addition to the precision matrix. As a result, the skewed Gaussian graphical model can be efficiently estimated through a penalized likelihood method just like the Gaussian graphical model. We develop an algorithm to maximize the penalized likelihood based on the alternating direction method of multipliers, and establish the asymptotic normality and variable selection consistency for the new estimator. Through simulations, we demonstrate that our method performs better than the Gaussian and Gaussian copula methods when these distributional assumptions are not satisfied. The method is applied to a breast cancer MicroRNA dataset to construct a gene network, which shows better interpretability than the Gaussian graphical model. In Chapter 5, we introduce a general cross-validation scheme, which we call "omnibus cross-validation", that applies to a wide class of estimation problems, including those with no response, no likelihood, and those which are not even of the form of an M-estimate. Traditional cross-validation usually involves prediction of a response variable: part of the data is used for model estimation, and the rest are held out for prediction, which determines the best set of parameters in variable selection, or the best tuning parameter for a variable selector. However, in many modern applications, such as the statistical graphical models, there are no response variables to predict, but only a likelihood to maximize. In other applications, there is not even a likelihood to maximize, but only a generic objective function to maximize. Although cross-validation has been applied naively to some of these situations, there is no systematic theory to back up such naive practices. We developed a systematic theory to support this new method, including Fisher consistency at population level, and asymptotic consistency at the sample level, both for best subset variable selection and for determining the tuning parameter through the solution path of existing variable selectors such as Lasso. We conduct simulation investigation of the performance of new method.
Author: Patrick Suppes
Publisher: Cambridge University Press
ISBN: 9780521568357
Category : Mathematics
Languages : en
Pages : 212
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Book Description
This is an important collection of essays by a leading philosopher, dealing with the foundations of probability.
