Entropy And Information Theory

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Entropy and Information Theory

Robert M. Gray
Entropy and Information Theory Book PDF

Author : Robert M. Gray
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 51,6 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475739824

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Entropy and Information Theory by Robert M. Gray Pdf

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.

New Foundations for Information Theory

David Ellerman
New Foundations for Information Theory Book PDF

Author : David Ellerman
Publisher : Springer Nature
Page : 121 pages
File Size : 45,6 Mb
Release : 2021-10-30
Category : Philosophy
ISBN : 9783030865528

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New Foundations for Information Theory by David Ellerman Pdf

This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.

Entropy and Information

Mikhail V. Volkenstein
Entropy and Information Book PDF

Author : Mikhail V. Volkenstein
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 49,9 Mb
Release : 2009-10-27
Category : Science
ISBN : 9783034600781

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Entropy and Information by Mikhail V. Volkenstein Pdf

This is just...entropy, he said, thinking that this explained everything, and he repeated the strange word a few times. 1 ? Karel Capek , “Krakatit” This “strange word” denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more universal concept, of fundamental signi?cance for chemistry and biology, as well as physics. Although the concept of energy is usually considered more important and easier to grasp, it turns out, as we shall see, that the idea of entropy is just as substantial—and moreover not all that complicated. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. Furthermore, entropy has remarkable properties. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium. Thereis a surprisingconnectionbetween entropyandinformation,thatis,thetotalintelligencecommunicatedbyamessage. All of this is expounded in the present book, thereby conveying informationto the readeranddecreasinghis entropy;butitis uptothe readertodecidehowvaluable this information might be.

Information Theory, Inference and Learning Algorithms

David J. C. MacKay
Information Theory Inference and Learning Algorithms Book PDF

Author : David J. C. MacKay
Publisher : Cambridge University Press
Page : 694 pages
File Size : 50,7 Mb
Release : 2003-09-25
Category : Computers
ISBN : 0521642981

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Information Theory, Inference and Learning Algorithms by David J. C. MacKay Pdf

Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Elements of Information Theory

Thomas M. Cover,Joy A. Thomas
Elements of Information Theory Book PDF

Author : Thomas M. Cover,Joy A. Thomas
Publisher : John Wiley & Sons
Page : 788 pages
File Size : 44,9 Mb
Release : 2012-11-28
Category : Computers
ISBN : 9781118585771

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Elements of Information Theory by Thomas M. Cover,Joy A. Thomas Pdf

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.

An Introduction to Transfer Entropy

Terry Bossomaier,Lionel Barnett,Michael Harré,Joseph T. Lizier
An Introduction to Transfer Entropy Book PDF

Author : Terry Bossomaier,Lionel Barnett,Michael Harré,Joseph T. Lizier
Publisher : Springer
Page : 190 pages
File Size : 45,7 Mb
Release : 2016-11-15
Category : Computers
ISBN : 9783319432229

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An Introduction to Transfer Entropy by Terry Bossomaier,Lionel Barnett,Michael Harré,Joseph T. Lizier Pdf

This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance. The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.

The Mathematical Theory of Communication

Claude E Shannon,Warren Weaver
The Mathematical Theory of Communication Book PDF

Author : Claude E Shannon,Warren Weaver
Publisher : University of Illinois Press
Page : 141 pages
File Size : 40,5 Mb
Release : 1998-09-01
Category : Language Arts & Disciplines
ISBN : 9780252098031

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The Mathematical Theory of Communication by Claude E Shannon,Warren Weaver Pdf

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Relative Information

Guy Jumarie
Relative Information Book PDF

Author : Guy Jumarie
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642840173

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Relative Information by Guy Jumarie Pdf

For four decades, information theory has been viewed almost exclusively as a theory based upon the Shannon measure of uncertainty and information, usually referred to as Shannon entropy. Since the publication of Shannon's seminal paper in 1948, the theory has grown extremely rapidly and has been applied with varied success in almost all areas of human endeavor. At this time, the Shannon information theory is a well established and developed body of knowledge. Among its most significant recent contributions have been the use of the complementary principles of minimum and maximum entropy in dealing with a variety of fundamental systems problems such as predic tive systems modelling, pattern recognition, image reconstruction, and the like. Since its inception in 1948, the Shannon theory has been viewed as a restricted information theory. It has often been argued that the theory is capable of dealing only with syntactic aspects of information, but not with its semantic and pragmatic aspects. This restriction was considered a v~rtue by some experts and a vice by others. More recently, however, various arguments have been made that the theory can be appropriately modified to account for semantic aspects of in formation as well. Some of the most convincing arguments in this regard are in cluded in Fred Dretske's Know/edge & Flow of Information (The M.LT. Press, Cambridge, Mass., 1981) and in this book by Guy lumarie.

A First Course in Information Theory

Raymond W. Yeung
A First Course in Information Theory Book PDF

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781441986085

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A First Course in Information Theory by Raymond W. Yeung Pdf

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.

Probability Space

Nancy Kress
Probability Space Book PDF

Author : Nancy Kress
Publisher : Tor Books
Page : 368 pages
File Size : 51,5 Mb
Release : 2004-01-05
Category : Fiction
ISBN : 9781466825253

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Probability Space by Nancy Kress Pdf

Nancy Kress cemented her reputation in SF with the publication of her multiple-award–winning novella, "Beggars in Spain," which became the basis for her extremely successful Beggars Trilogy (comprising Beggars in Spain, Beggars and Choosers, and Beggars Ride). And now she brings us Probability Space, the conclusion of the trilogy that began with Probability Moon and then Probability Sun, which is centered on the same world as Kress's Nebula Award-winning novelette, "Flowers of Aulit Prison." The Probability Trilogy has already been widely recognized as the next great work by this important SF writer. In Probability Space, humanity's war with the alien Fallers continues, and it is a war we are losing. Our implacable foes ignore all attempts at communication, and they take no prisoners. Our only hope lies with an unlikely coalition: Major Lyle Kaufman, retired warrior; Marbet Grant, the Sensitive who's involved with Kaufman; Amanda, a very confused fourteen-year-old girl; and Magdalena, one of the biggest power brokers in all of human space. As the action moves from Earth to Mars to the farthest reaches of known space, with civil unrest back home and alien war in deep space, four humans--armed with little more than an unproven theory--try to enter the Fallers' home star system. It's a desperate gamble, and the fate of the entire universe may hang in the balance. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

Science and Information Theory

Leon Brillouin
Science and Information Theory Book PDF

Author : Leon Brillouin
Publisher : Courier Corporation
Page : 370 pages
File Size : 45,9 Mb
Release : 2013-07-17
Category : Science
ISBN : 9780486497556

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Science and Information Theory by Leon Brillouin Pdf

Geared toward upper-level undergraduates and graduate students, this classic resource by a giant of 20th-century mathematics applies principles of information theory to Maxwell's demon, thermodynamics, and measurement problems. 1962 edition.

Mathematical Foundations of Information Theory

Aleksandr I?Akovlevich Khinchin
Mathematical Foundations of Information Theory Book PDF

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 130 pages
File Size : 45,7 Mb
Release : 1957-01-01
Category : Mathematics
ISBN : 9780486604343

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Mathematical Foundations of Information Theory by Aleksandr I?Akovlevich Khinchin Pdf

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.

Information Theory

Imre Csiszár,János Körner
Information Theory Book PDF

Author : Imre Csiszár,János Körner
Publisher : Elsevier
Page : 465 pages
File Size : 41,9 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483281575

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Information Theory by Imre Csiszár,János Körner Pdf

Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon’s information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science.

Probability for Machine Learning

Jason Brownlee
Probability for Machine Learning Book PDF

Author : Jason Brownlee
Publisher : Machine Learning Mastery
Page : 319 pages
File Size : 50,8 Mb
Release : 2019-09-24
Category : Computers
ISBN : 8210379456XXX

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Probability for Machine Learning by Jason Brownlee Pdf

Probability is the bedrock of machine learning. You cannot develop a deep understanding and application of machine learning without it. Cut through the equations, Greek letters, and confusion, and discover the topics in probability that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover the importance of probability to machine learning, Bayesian probability, entropy, density estimation, maximum likelihood, and much more.

The Mathematical Theory of Information

Jan Kåhre
The Mathematical Theory of Information Book PDF

Author : Jan Kåhre
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 42,9 Mb
Release : 2002-06-30
Category : Technology & Engineering
ISBN : 1402070640

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The Mathematical Theory of Information by Jan Kåhre Pdf

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.