Information Theory and the Central Limit Theorem

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.

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Author: Oliver Thomas Johnson

Publisher: World Scientific

ISBN: 9781860944734

Category: Mathematics

Page: 209

View: 778

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 It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.

Information Theory and the Central Limit Theorem

Now ( Rényi , 1961 ) promises that another paper will provide “ a simplified
version of Linnik's information - theoretic proof of the Central Limit Theorem ” .
Commenting on this , in his note after this paper , ( Csiszár , 1976 ) points out that
Rényi ...

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Author: Oliver Johnson

Publisher: World Scientific

ISBN: 1860945376

Category: Computers

Page: 224

View: 901

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.

Information Theory

The extreme variability in the final odds that a signal is present is an aspect of the
approximate lognormality of the odds , which itself will often be a consequence of
the additivity of weights of evidence , in virtue of the Central Limit Theorem .

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Author: Sir Willis Jackson

Publisher:

ISBN: UIUC:30112008120328

Category: Information theory

Page:

View: 758

Relative Information

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.

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Author: Guy Jumarie

Publisher: Springer Science & Business Media

ISBN: 9783642840173

Category: Science

Page: 258

View: 662

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.

Transactions of the Seventh Prague Conference on Information Theory Statistical Decision Functions Random Processes and of the 1974 European Meeting of Statisticians Held at Prague from August 18 to 23 1974

REFERENCES [ 1 ] P. BILLINGSLEY : Convergence of probability measures .
Wiley , New York 1968 . [ 2 ] B. M. BROWN : Martingale central limit theorems .
Ann . Math . Statist . 42 ( 1971 ) , 1 , 59-66 . [ 3 ] M. CSÖRGÖ & S. CSÖRGÖ : On ...

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Author:

Publisher:

ISBN: UVA:X000600960

Category: Information Theory

Page: 602

View: 997

Information theory statistical decision functions random processes

This paper contains a limit theorem for discrete SMRE . Limit theorems for SMRE
in asymptotic phase merging scheme have been considered in Swishchuk ( 1985
) and Koroljuk , Swishchuk ( 1988 ) . A central Limit Theorem for SMRE was ...

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Author: Jan Ámos Víšek

Publisher: Springer

ISBN: 0792311191

Category: Science

Page: 498

View: 618

Probability and Information

Solutions are available by email. This book is suitable as a textbook for beginning students in mathematics, statistics, or computer science who have some knowledge of basic calculus.

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Author: David Applebaum

Publisher: Cambridge University Press

ISBN: 0521555078

Category: Mathematics

Page: 226

View: 493

This elementary introduction to probability theory and information theory provides a clear and systematic foundation to the subject; the author pays particular attention to the concept of probability via a highly simplified discussion of measures on Boolean algebras. He then applies the theoretical ideas to practical areas such as statistical inference, random walks, statistical mechanics, and communications modeling. Applebaum deals with topics including discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem, and the coding and transmission of information. The author includes many examples and exercises that illustrate how the theory can be applied, e.g. to information technology. Solutions are available by email. This book is suitable as a textbook for beginning students in mathematics, statistics, or computer science who have some knowledge of basic calculus.

System Engineering Handbook

It has been pointed out * that “ information theory will probably always remain ,
like thermodynamics , conceptual and guiding rather than ... V . Linnik , where a
novel proof of the central - limit theorem based on information theory is derived .

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Author: Robert Engel Machol

Publisher:

ISBN: UOM:39015004569516

Category: Systems engineering

Page: 1066

View: 388

Publicationes mathematicae

On a theorem of P. Erdős and its application in information theory . On the
dimension and entropy of probability distributions . New version of the
probabilistic generalization of the Large Sieve . On the central limit theorem for
samples from a ...

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Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet

Publisher:

ISBN: UCAL:B3530149

Category: Mathematics

Page:

View: 315

Computers Control Information Theory

Information Sciences and Systems Lab . cific attention is given to log - likelihood
ratio detectors . The 1985 , 8p Pub . in IEEE International Radar Conference ,
question is discussed as to whether a Central Limit Theorem p297-302 1985 .

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Author:

Publisher:

ISBN: IND:30000100120314

Category: Computers

Page:

View: 636

The Life and Times of the Central Limit Theorem

About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making.

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Author: William J. Adams

Publisher: American Mathematical Soc.

ISBN: 9780821848999

Category: Mathematics

Page: 195

View: 252

About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making. --Philip Peak, The Mathematics Teacher, May, 1975 I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics. --Wei-Ching Chang, Historica Mathematica, August, 1976 In the months since I wrote ... I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics. --Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975 The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of The Life and Times of the Central Limit Theorem, Second Edition traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of $\exp (x^2)$ as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.

Black Engineers in the United States a Directory

Honors : Tau Beta Pi , White House Fellowship . Publications : " Singular Non -
Gaussian Measures in Detection and Estimation Theory , " IEEE Trans on
Information Theory , Mar 1969 ; " New Conditions for Central Limit Theorems , "
Annals of ...

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Author: James K. K. Ho

Publisher:

ISBN: UOM:39015007666517

Category: Technology & Engineering

Page: 281

View: 294

Proceedings IEEE International Symposium on Information Theory

Entropy Computations for Discrete Distributions : Towards Analytic Information
Theory Philippe Jacquet Wojciech ... a class of sequences of discrete distribution
Pn , satisfying the central limit theorem for which the moment generating function
 ...

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Author:

Publisher:

ISBN: PSU:000032297294

Category: Information theory

Page:

View: 459

Bounds on the Sample Complexity of Bayesian Learning Using Information Theory and the VC Dimension

( 7 ) B. Clarke and A. Barron . Entropy , risk and the Bayesian central limit
theorem . manuscript . [ 8 ] B. Clarke and A. Barron . Information - theoretic
asymptotics of Bayes methods . IEEE Transactions on Information Theory , 36 ( 3
) : 453–471 ...

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Author: David Haussler

Publisher:

ISBN: UCSC:32106020335169

Category: Machine learning

Page: 29

View: 948

Abstract: "In this paper we study a Bayesian or average-case model of concept learning with a twofold goal: to provide more precise characterizations of learning curve (sample complexity) behavior that depend on properties of both the prior distribution over concepts and the sequence of instances seen by the learner, and to smmoothly unite in a common framework the popular statistical physics and VC dimension theories of learning curves. To achieve this, we undertake a systematic investigation and comparison of two fundamental quantities in learning and information theory: the probability of an incorrect prediction for an optimal learning algorithm, and the Shannon information gain. This study leads to a new understanding of the sample complexity of learning in several existing models."

Probability in Banach Spaces III

Giné , E ( 1974 ) On the central limit theorem for sample continuous processes . ...
The strong law of large numbers and the central limit theorem in Banach spaces .
... The central limit theorem and ε - entropy , Prob . and information theory .

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Author: A. Beck

Publisher: Springer

ISBN: 354010822X

Category: Mathematics

Page: 332

View: 121

Transactions of the IRE Professional Group on Information Theory

Professional Group on Information Theory. THE RESPONSE OF LINEAR ... Since
y ( t ) is the sum of independent inputs , it will tend towards the Gaussian in most
cases , i.e. , when the central limit theorem holds . Furthermore , the variance of ...

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Author: Institute of Radio Engineers. Professional Group on Information Theory

Publisher:

ISBN: CORNELL:31924057735833

Category: Information theory

Page:

View: 347

Transactions of the I R E Professional Group on Information Theory

I.R.E. Professional Group on Information Theory. THE RESPONSE OF ... Since y (
t ) is the sum of independent inputs , it will tend towards the Gaussian in most
cases , i.e. , when the central limit theorem holds . Furthermore , the variance of y
 ...

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Author: I.R.E. Professional Group on Information Theory

Publisher:

ISBN: UIUC:30112008095694

Category: Information theory

Page:

View: 399

IRE Transactions on Information Theory

The absolute value of D Noise Gaussian V2 / 1.65 V271 is less than 0.8 and it is
less than 0.28 for limiting levels above ... While the edge of the input noise band
than at its center . the central limit theorem applies to the noise times noise terms
 ...

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Author:

Publisher:

ISBN: UCR:31210010785184

Category: Information theory

Page:

View: 967