## Information Theory and Statistical Learning

**Author**: Frank Emmert-Streib,Matthias Dehmer

**Publisher:**Springer Science & Business Media

**ISBN:**0387848150

**Category:**Computers

**Page:**439

**View:**3129

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This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.

## Information Theory and Statistics

**Author**: Solomon Kullback

**Publisher:**Courier Corporation

**ISBN:**0486142043

**Category:**Mathematics

**Page:**416

**View:**1032

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Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.

## Information Theory and Statistics

*A Tutorial*

**Author**: Imre Csiszár,Paul C. Shields

**Publisher:**Now Publishers Inc

**ISBN:**9781933019055

**Category:**Computers

**Page:**115

**View:**5533

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Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.

## Basic concepts in information theory and statistics

*axiomatic foundations and applications*

**Author**: A. M. Mathai,P. N. Rathie

**Publisher:**Halsted Press

**ISBN:**N.A

**Category:**Mathematics

**Page:**137

**View:**8908

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## Elements of Information Theory

**Author**: Thomas M. Cover,Joy A. Thomas

**Publisher:**John Wiley & Sons

**ISBN:**1118585771

**Category:**Computers

**Page:**776

**View:**6195

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The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.

## Stochastic Models, Information Theory, and Lie Groups, Volume 2

*Analytic Methods and Modern Applications*

**Author**: Gregory S. Chirikjian

**Publisher:**Springer Science & Business Media

**ISBN:**0817649433

**Category:**Mathematics

**Page:**435

**View:**9612

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This two-volume set covers stochastic processes, information theory and Lie groups in a unified setting, bridging topics rarely studied together. The emphasis is on using stochastic, geometric, and group-theoretic concepts for modeling physical phenomena.

## An Introduction to Information Theory

**Author**: Fazlollah M. Reza

**Publisher:**Courier Corporation

**ISBN:**0486158446

**Category:**Mathematics

**Page:**528

**View:**2619

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Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.

## Stochastic Models, Information Theory, and Lie Groups, Volume 1

*Classical Results and Geometric Methods*

**Author**: Gregory S. Chirikjian

**Publisher:**Birkhäuser

**ISBN:**9780817648022

**Category:**Mathematics

**Page:**383

**View:**4941

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This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

## Information Theory and the Central Limit Theorem

**Author**: Oliver Johnson

**Publisher:**World Scientific

**ISBN:**9781860945373

**Category:**Computers

**Page:**224

**View:**3156

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Annotation. - Presents surprising, interesting connections between two apparently separate areas of mathematics- Written by one of the researchers who discovered these connections- Offers a new way of looking at familiar results.

## Elements of Information Theory

**Author**: Cover

**Publisher:**John Wiley & Sons

**ISBN:**9788126508143

**Category:**

**Page:**566

**View:**9877

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· Entropy, Relative Entropy and Mutual Information· The Asymptotic Equipartition Property· Entropy Rates of a Stochastic Process· Data Compression· Gambling and Data Compression· Kolmogorov Complexity· Channel Capacity· Differential Entropy· The Gaussian Channel· Maximum Entropy and Spectral Estimation· Information Theory and Statistics· Rate Distortion Theory· Network Information Theory· Information Theory and the Stock Market· Inequalities in Information Theory

## Advances in Inequalities from Probability Theory and Statistics

**Author**: Neil S. Barnett

**Publisher:**Nova Publishers

**ISBN:**9781600219436

**Category:**Inequalities (Mathematics)

**Page:**227

**View:**5947

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This is the first in a series of research monographs that focus on the research, development and use of inequalities in probability and statistics. All of the papers have been peer refereed and this first edition covers a range of topics that include both survey material of published work as well as new results appearing in print for the first time.

## Statistical Theory Of Communication

**Author**: S.P. Eugene Xavier

**Publisher:**New Age International

**ISBN:**9788122411270

**Category:**

**Page:**508

**View:**8341

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This Book Deals With The Application Of Statistics To Communication Systems And Radar Signal Processing. Information Theory, Coding, Random Processes, Optimum Linear Systems And Estimation Theory Forms The Subject Matter Of This Book. The Subject Treatment Requires A Basic Knowledge Of Probability And Statistics. This Book Is Intended As A Text For A Graduate Level Course On Electronics And Communication Engineering.

## Information Theory for Continuous Systems

**Author**: Shunsuke Ihara

**Publisher:**World Scientific

**ISBN:**9789810209858

**Category:**Computers

**Page:**308

**View:**5924

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This book provides a systematic mathematical analysis of entropy and stochastic processes, especially Gaussian processes, and its applications to information theory.The contents fall roughly into two parts. In the first part a unified treatment of entropy in information theory, probability theory and mathematical statistics is presented. The second part deals mostly with information theory for continuous communication systems. Particular emphasis is placed on the Gaussian channel.An advantage of this book is that, unlike most books on information theory, it places emphasis on continuous communication systems, rather than discrete ones.

## Entropy and Information Theory

**Author**: Robert M. Gray

**Publisher:**Springer Science & Business Media

**ISBN:**1475739826

**Category:**Computers

**Page:**332

**View:**8102

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This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.

## Information Theory and the Central Limit Theorem

**Author**: Oliver Johnson

**Publisher:**World Scientific

**ISBN:**1783260610

**Category:**Mathematics

**Page:**224

**View:**7398

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This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. Contents:Introduction to Information TheoryConvergence in Relative EntropyNon-Identical Variables and Random VectorsDependent Random VariablesConvergence to Stable LawsConvergence on Compact GroupsConvergence to Poisson DistributionFree Random Variables Readership: Graduate students, academics and researchers in probability and statistics. Key Features:Presents surprising, interesting connections between two apparently separate areas of mathematicsWritten by one of the researchers who discovered these connectionsOffers a new way of looking at familiar resultsKeywords:Information Theory;Entropy;Fisher Information;Central Limit Theorem;Probability;Statistics;Convergence of Random VariablesReviews:“This book provides a well-written and motivating introduction to information theory and a detailed description of the current research regarding the connections between central limit theorems and information theory. It is an important reference for many graduate students and researchers in this domain.”Mathematical Reviews

## Coding and Information Theory

**Author**: Steven Roman

**Publisher:**Springer Science & Business Media

**ISBN:**9780387978123

**Category:**Mathematics

**Page:**488

**View:**3635

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This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.

## Concepts of Probability Theory

**Author**: Paul E. Pfeiffer

**Publisher:**Courier Corporation

**ISBN:**0486636771

**Category:**Mathematics

**Page:**405

**View:**1987

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Using the simple conceptual framework of the Kolmogorov model, this intermediate-level textbook discusses random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. For advanced undergraduate students of science, engineering, or mathematics acquainted with basic calculus. Includes problems with answers and six appendixes. 1965 edition.

## Statistical Implications of Turing's Formula

**Author**: Zhiyi Zhang

**Publisher:**John Wiley & Sons

**ISBN:**1119237068

**Category:**Mathematics

**Page:**296

**View:**3942

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Features a broad introduction to recent research on Turing’s formula and presents modern applications in statistics, probability, information theory, and other areas of modern data science Turing's formula is, perhaps, the only known method for estimating the underlying distributional characteristics beyond the range of observed data without making any parametric or semiparametric assumptions. This book presents a clear introduction to Turing’s formula and its connections to statistics. Topics with relevance to a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence and machine learning; big data; biology; ecology; and genetics. The author provides examinations of many core statistical issues within modern data science from Turing's perspective. A systematic approach to long-standing problems such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation is presented in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author provides a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach derived from Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate certain heavy-tailed distributions. In summary, this book: • Features a unified and broad presentation of Turing’s formula, including its connections to statistics, probability, information theory, and other areas of modern data science • Provides a presentation on the statistical estimation of information theoretic quantities • Demonstrates the estimation problems of several statistical functions from Turing's perspective such as Simpson's indices, Shannon's entropy, general diversity indices, mutual information, and Kullback–Leibler divergence • Includes numerous exercises and examples throughout with a fundamental perspective on the key results of Turing’s formula Statistical Implications of Turing's Formula is an ideal reference for researchers and practitioners who need a review of the many critical statistical issues of modern data science. This book is also an appropriate learning resource for biologists, ecologists, and geneticists who are involved with the concept of diversity and its estimation and can be used as a textbook for graduate courses in mathematics, probability, statistics, computer science, artificial intelligence, machine learning, big data, and information theory. Zhiyi Zhang, PhD, is Professor of Mathematics and Statistics at The University of North Carolina at Charlotte. He is an active consultant in both industry and government on a wide range of statistical issues, and his current research interests include Turing's formula and its statistical implications; probability and statistics on countable alphabets; nonparametric estimation of entropy and mutual information; tail probability and biodiversity indices; and applications involving extracting statistical information from low-frequency data space. He earned his PhD in Statistics from Rutgers University.

## Information Theory and Coding by Example

**Author**: Mark Kelbert,Yuri Suhov

**Publisher:**Cambridge University Press

**ISBN:**0521769353

**Category:**Computers

**Page:**526

**View:**7524

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A valuable teaching aid. Provides relevant background material, many examples and clear solutions to problems taken from real exam papers.