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Author: Ruslan L. Stratonovich
Publisher: Springer Nature
ISBN: 3030228339
Category : Mathematics
Languages : en
Pages : 419
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Book Description
This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or 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
Table of contents
Author: Ruslan L. Stratonovich
Publisher: Springer Nature
ISBN: 3030228339
Category : Mathematics
Languages : en
Pages : 419
Get Book
Book Description
This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.
Author: Mark Burgin
Publisher: World Scientific
ISBN: 9812835490
Category : Computers
Languages : en
Pages : 689
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Book Description
This unique volume presents a new approach OCo the general theory of information OCo to scientific understanding of information phenomena. Based on a thorough analysis of information processes in nature, technology, and society, as well as on the main directions in information theory, this theory synthesizes existing directions into a unified system. The book explains how this theory opens new kinds of possibilities for information technology, information sciences, computer science, knowledge engineering, psychology, linguistics, social sciences, and education. The book also gives a broad introduction to the main mathematically-based directions in information theory. The general theory of information provides a unified context for existing directions in information studies, making it possible to elaborate on a comprehensive definition of information; explain relations between information, data, and knowledge; and demonstrate how different mathematical models of information and information processes are related. Explanation of information essence and functioning is given, as well as answers to the following questions: how information is related to knowledge and data; how information is modeled by mathematical structures; how these models are used to better understand computers and the Internet, cognition and education, communication and computation. Sample Chapter(s). Chapter 1: Introduction (354 KB). Contents: General Theory of Information; Statistical Information Theory; Semantic Information Theory; Algorithm Information Theory; Pragmatic Information Theory; Dynamics of Information. Readership: Professionals in information processing, and general readers interested in information and information processes.
Author: Thomas M. Cover
Publisher: John Wiley & Sons
ISBN: 1118585771
Category : Computers
Languages : en
Pages : 788
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Book Description
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.
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486604349
Category : Mathematics
Languages : en
Pages : 130
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Book Description
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author: Robert B. Ash
Publisher: Halsted Press
ISBN:
Category : Computers
Languages : en
Pages : 360
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Book Description
Author: Jan Kåhre
Publisher: Springer Science & Business Media
ISBN: 9781402070648
Category : Technology & Engineering
Languages : en
Pages : 528
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Book Description
The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.
Author: JV Stone
Publisher: Sebtel Press
ISBN: 0956372856
Category : Business & Economics
Languages : en
Pages : 243
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Book Description
Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.
Author: Robert M. Gray
Publisher: Springer Science & Business Media
ISBN: 1475739826
Category : Computers
Languages : en
Pages : 346
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Book Description
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.
Author: Raymond W. Yeung
Publisher: Springer Science & Business Media
ISBN: 1441986081
Category : Technology & Engineering
Languages : en
Pages : 426
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Book Description
This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.
