discrete probability models and methods probability on graphs and trees markov chains and random fields entropy and coding probability theory and stochastic modelling

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Discrete Probability Models And Methods

Author : Pierre Brémaud
ISBN : 9783319434766
Genre : Mathematics
File Size : 87. 44 MB
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The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

Stochastic Modeling

Author : Nicolas Lanchier
ISBN : 9783319500386
Genre : Mathematics
File Size : 55. 24 MB
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Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and MatlabTM.

Graphical Models Exponential Families And Variational Inference

Author : Martin J. Wainwright
ISBN : 9781601981844
Genre : Computers
File Size : 44. 7 MB
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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.

Random Measures Theory And Applications

Author : Olav Kallenberg
ISBN : 9783319415987
Genre : Mathematics
File Size : 71. 48 MB
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Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.

A Stochastic Grammar Of Images

Author : Song-Chun Zhu
ISBN : 9781601980601
Genre : Computers
File Size : 44. 33 MB
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A stochastic Grammar of Image is the first book to provide a foundational review and perspective of grammatical approaches to computer vision in its quest for a stochastic and context sensitive grammar of images, if is intended to serve as a unified frame work of representation leaming and recognition for a large number of object categories. It starts out by addressing he historic trends in the area and overviewing the main concepts such as the and or graph the parse graphs the dictionary and goes on to learning issues, semantic gaps between symbols and pixels dataset for for learning and algorithms. The proposal grammar presented integrates three prominent representations in the literature stochastic grammar for composition. Markev (or graphical) models for contexts, and sparse coding with primitives (wavelets). It also combines the structure-based and appearance based methods in the vision literature. At the end of the review three case studies are presented to illustrate the proposed grammar. A Stochastic Grammar of Images is an important contribution to the literature on structured statistical models in computer vision.

Machine Learning

Author : Kevin P. Murphy
ISBN : 9780262018029
Genre : Computers
File Size : 42. 18 MB
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A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach.

An Introduction To Conditional Random Fields

Author : Charles Sutton
ISBN : 160198572X
Genre : Computers
File Size : 36. 29 MB
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An Introduction to Conditional Random Fields provides a comprehensive tutorial aimed at application-oriented practitioners seeking to apply CRFs. The monograph does not assume previous knowledge of graphical modeling, and so is intended to be useful to practitioners in a wide variety of fields.

Random Graphs And Complex Networks

Author : Remco van der Hofstad
ISBN : 9781107172876
Genre : Computers
File Size : 30. 99 MB
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This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Bayesian Reasoning And Machine Learning

Author : David Barber
ISBN : 9780521518147
Genre : Computers
File Size : 81. 12 MB
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A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.

Probabilistic Graphical Models

Author : Daphne Koller
ISBN : 9780262258357
Genre : Computers
File Size : 35. 71 MB
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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.

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