Stochastic Complexity In Statistical Inquiry Theory

Author : Jorma Rissanen
Publisher : World Scientific
Page : 191 pages
File Size : 48,7 Mb
Release : 1998-10-07
Category : Technology & Engineering
ISBN : 9789814507400

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Stochastic Complexity In Statistical Inquiry by Jorma Rissanen Pdf

This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.

Author : Jorma Rissanen
Publisher : World Scientific Publishing Company Incorporated
Page : 188 pages
File Size : 52,5 Mb
Release : 1989-08-01
Category : Business & Economics
ISBN : 981020311X

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Stochastic Complexity in Statistical Inquiry Theory by Jorma Rissanen Pdf

Author : Jorma Rissanen
Publisher : World Scientific Publishing Company Incorporated
Page : 177 pages
File Size : 40,6 Mb
Release : 1989-01-01
Category : Business & Economics
ISBN : 9971508591

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Stochastic Complexity in Statistical Inquiry by Jorma Rissanen Pdf

Author : Jorma Rissanen
Publisher : Springer Science & Business Media
Page : 145 pages
File Size : 51,5 Mb
Release : 2007-12-15
Category : Mathematics
ISBN : 9780387688121

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Information and Complexity in Statistical Modeling by Jorma Rissanen Pdf

No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.

Author : David J. Hand
Publisher : CRC Press
Page : 431 pages
File Size : 43,9 Mb
Release : 2020-11-26
Category : Business & Economics
ISBN : 9781000152913

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Artificial Intelligence Frontiers in Statistics by David J. Hand Pdf

This book presents a summary of recent work on the interface between artificial intelligence and statistics. It does this through a series of papers by different authors working in different areas of this interface. These papers are a selected and referenced subset of papers presented at the 3rd Interntional Workshop on Artificial Intelligence and Statistics, Florida, January 1991.

Author : Wojciech H. Zurek
Publisher : CRC Press
Page : 545 pages
File Size : 43,8 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429971433

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Complexity, Entropy And The Physics Of Information by Wojciech H. Zurek Pdf

This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.

Author : Ming Li,Paul Vitányi
Publisher : Springer
Page : 834 pages
File Size : 52,6 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 9783030112981

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An Introduction to Kolmogorov Complexity and Its Applications by Ming Li,Paul Vitányi Pdf

This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.

Author : Peter D. Grünwald,In Jae Myung,Mark A. Pitt
Publisher : MIT Press
Page : 464 pages
File Size : 54,7 Mb
Release : 2005
Category : Computers
ISBN : 0262072629

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Advances in Minimum Description Length by Peter D. Grünwald,In Jae Myung,Mark A. Pitt Pdf

A source book for state-of-the-art MDL, including an extensive tutorial and recent theoretical advances and practical applications in fields ranging from bioinformatics to psychology.

Author : P. Grassberger,J.P. Nadal
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401110686

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From Statistical Physics to Statistical Inference and Back by P. Grassberger,J.P. Nadal Pdf

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Author : Andreas Greven,Gerhard Keller,Gerald Warnecke
Publisher : Princeton University Press
Page : 376 pages
File Size : 44,5 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865222

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Entropy by Andreas Greven,Gerhard Keller,Gerald Warnecke Pdf

The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.

Author : Hamparsum Bozdogan
Publisher : CRC Press
Page : 624 pages
File Size : 49,5 Mb
Release : 2003-07-29
Category : Business & Economics
ISBN : 9780203497159

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Statistical Data Mining and Knowledge Discovery by Hamparsum Bozdogan Pdf

Massive data sets pose a great challenge to many cross-disciplinary fields, including statistics. The high dimensionality and different data types and structures have now outstripped the capabilities of traditional statistical, graphical, and data visualization tools. Extracting useful information from such large data sets calls for novel approache

Author : Peter D. Grünwald
Publisher : MIT Press
Page : 736 pages
File Size : 46,5 Mb
Release : 2007
Category : Minimum description length (Information theory).
ISBN : 9780262072816

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The Minimum Description Length Principle by Peter D. Grünwald Pdf

This introduction to the MDL Principle provides a reference accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.

Author : Claude Sammut,Geoffrey I. Webb
Publisher : Springer Science & Business Media
Page : 1061 pages
File Size : 47,9 Mb
Release : 2011-03-28
Category : Computers
ISBN : 9780387307688

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Encyclopedia of Machine Learning by Claude Sammut,Geoffrey I. Webb Pdf

This comprehensive encyclopedia, in A-Z format, provides easy access to relevant information for those seeking entry into any aspect within the broad field of Machine Learning. Most of the entries in this preeminent work include useful literature references.

Author : David Brillinger,Peter Caines,John Geweke,Emanuel Parzen,Murray Rosenblatt,Murad S. Taqqu
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461392965

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New Directions in Time Series Analysis by David Brillinger,Peter Caines,John Geweke,Emanuel Parzen,Murray Rosenblatt,Murad S. Taqqu Pdf

This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l.

Author : Paul Smolensky,Michael C. Mozer
Publisher : Psychology Press
Page : 865 pages
File Size : 47,5 Mb
Release : 2013-05-13
Category : Psychology
ISBN : 9781134772940

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Mathematical Perspectives on Neural Networks by Paul Smolensky,Michael C. Mozer Pdf

Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.