Information Theory Meets Power Laws: Stochastic Processes and Language Models by

Description: FREE SHIPPING UK WIDE Information Theory Meets Power Laws by Lukasz Debowski Discover new theoretical connections between stochastic phenomena and the structure of natural language with this powerful volume! Information Theory Meets Power Laws: Stochastic Processes and Language Models presents readers with a novel subtype of a probabilistic approach to language, which is based on statistical laws of texts and their analysis by means of information theory. The distinguished author insightfully and rigorously examines the linguistic and mathematical subject matter while eschewing needlessly abstract and superfluous constructions. The book begins with a less formal treatment of its subjects in the first chapter, introducing its concepts to readers without mathematical training and allowing those unfamiliar with linguistics to learn the books motivations. Despite its inherent complexity, Information Theory Meets Power Laws: Stochastic Processes and Language Models is a surprisingly approachable treatment of idealized mathematical models of human language. The author succeeds in developing some of the theory underlying fundamental stochastic and semantic phenomena, like strong nonergodicity, in a way that has not previously been seriously attempted. In doing so, he covers topics including: Zipfs and Herdans laws for natural languagePower laws for information, repetitions, and correlationsMarkov, finite-state,and Santa Fe processesBayesian and frequentist interpretations of probabilityErgodic decomposition, Kolmogorov complexity, and universal codingTheorems about facts and wordsInformation measures for fieldsRényi entropies, recurrence times, and subword complexityAsymptotically mean stationary processes Written primarily for mathematics graduate students and professionals interested in information theory or discrete stochastic processes, Information Theory Meets Power Laws: Stochastic Processes and Language Models also belongs on the bookshelves of doctoral students and researchers in artificial intelligence, computational and quantitative linguistics as well as physics of complex systems. FORMAT Hardcover LANGUAGE English CONDITION Brand New Back Cover Discover new theoretical connections between stochastic phenomena and the structure of natural language with this powerful volume Information Theory Meets Power Laws: Stochastic Processes and Language Models presents readers with a novel subtype of a probabilistic approach to language, which is based on statistical laws of texts and their analysis by means of information theory. The distinguished author insightfully and rigorously examines the linguistic and mathematical subject matter while eschewing needlessly abstract and superfluous constructions. The book begins with a less formal treatment of its subjects in the first chapter, introducing its concepts to readers without mathematical training and allowing those unfamiliar with linguistics to learn the books motivations. Despite its inherent complexity, Information Theory Meets Power Laws: Stochastic Processes and Language Models is a surprisingly approachable treatment of idealized mathematical models of human language. The author succeeds in developing some of the theory underlying fundamental stochastic and semantic phenomena, like strong nonergodicity, in a way that has not previously been attempted. In doing so, he covers topics including: Zipfs and Herdans laws for natural language Power laws for information, repetitions, and correlations Markov, finite-state, and Santa Fe processes Bayesian and frequentist interpretations of probability Ergodic decomposition, Kolmogorov complexity, and universal coding Theorems about facts and words Information measures for fields R Flap Discover new theoretical connections between stochastic phenomena and the structure of natural language with this powerful volume Information Theory Meets Power Laws: Stochastic Processes and Language Models presents readers with a novel subtype of a probabilistic approach to language, which is based on statistical laws of texts and their analysis by means of information theory. The distinguished author insightfully and rigorously examines the linguistic and mathematical subject matter while eschewing needlessly abstract and superfluous constructions. The book begins with a less formal treatment of its subjects in the first chapter, introducing its concepts to readers without mathematical training and allowing those unfamiliar with linguistics to learn the books motivations. Despite its inherent complexity, Information Theory Meets Power Laws: Stochastic Processes and Language Models is a surprisingly approachable treatment of idealized mathematical models of human language. The author succeeds in developing some of the theory underlying fundamental stochastic and semantic phenomena, like strong nonergodicity, in a way that has not previously been attempted. In doing so, he covers topics including: Zipfs and Herdans laws for natural language Power laws for information, repetitions, and correlations Markov, finite-state, and Santa Fe processes Bayesian and frequentist interpretations of probability Ergodic decomposition, Kolmogorov complexity, and universal coding Theorems about facts and words Information measures for fields R Author Biography UKASZ DBOWSKI, PHD, works at the Institute of Computer Science of the Polish Academy of Sciences in Poland. His doctorate is in mathematics and computer science and his primary research focus is in the areas of information theory and discrete stochastic processes. He is also interested in the theoretical properties of statistical and neural language models. Table of Contents Preface ix Acknowledgments xiii Basic Notations xv 1 Guiding Ideas 1 1.1 The Motivating Question 1 1.2 Further Questions About Texts 5 1.3 Zipfs and Herdans Laws 8 1.4 Markov and Finite-State Processes 14 1.5 More General Stochastic Processes 20 1.6 Two Interpretations of Probability 23 1.7 Insights from Information Theory 25 1.8 Estimation of Entropy Rate 28 1.9 Entropy of Natural Language 30 1.10 Algorithmic Information Theory 35 1.11 Descriptions of a Random World 37 1.12 Facts and Words Related 43 1.13 Repetitions and Entropies 47 1.14 Decay of Correlations 52 1.15 Recapitulation 54 2 Probabilistic Preliminaries 57 2.1 Probability Measures 59 2.2 Product Measurable Spaces 63 2.3 Discrete Random Variables 65 2.4 From IID to Finite-State Processes 68 Problems 73 3 Probabilistic Toolbox 77 3.1 Borel Details ISBN1119625270 ISBN-10 1119625270 ISBN-13 9781119625278 Format Hardcover Short Title Information Theory Meets Power Laws Language English Subtitle Stochastic Processes and Language Models Year 2021 DEWEY 410.15195 Pages 384 Publication Date 2021-04-08 UK Release Date 2021-04-08 Country of Publication United States AU Release Date 2021-04-08 NZ Release Date 2021-04-08 US Release Date 2021-04-08 Author Lukasz Debowski Publisher John Wiley & Sons Inc Imprint John Wiley & Sons Inc Place of Publication New York Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. 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