Quantum Statistical Inference for Density Estimation
Quantum Statistical Inference for Density Estimation

Author:

Publisher:

Published: 1993

Total Pages: 10

ISBN-13:

DOWNLOAD EBOOK

A new penalized likelihood method for non-parametric density estimation is proposed, which is based on a mathematical analogy to quantum statistical physics. The mathematical procedure for density estimation is related to maximum entropy methods for inverse problems; the penalty function is a convex information divergence enforcing global smoothing toward default models, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing may be enforced by constraints on the expectation values of differential operators. Although the hyperparameters, covariance, and linear response to perturbations can be estimated by a variety of statistical methods, we develop the Bayesian interpretation. The linear response of the MAP estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood. The method is demonstrated on standard data sets.

Asymptotic Theory Of Quantum Statistical Inference: Selected Papers
Asymptotic Theory Of Quantum Statistical Inference: Selected Papers

Author: Masahito Hayashi

Publisher: World Scientific

Published: 2005-02-21

Total Pages: 553

ISBN-13: 981448198X

DOWNLOAD EBOOK

Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.

Nonparametric Density Estimation
Nonparametric Density Estimation

Author: Luc Devroye

Publisher: New York ; Toronto : Wiley

Published: 1985-01-18

Total Pages: 376

ISBN-13:

DOWNLOAD EBOOK

This book gives a rigorous, systematic treatment of density estimates, their construction, use and analysis with full proofs. It develops L1 theory, rather than the classical L2, showing how L1 exposes fundamental properties of density estimates masked by L2.

Density Estimation by Maximum Quantum Entropy
Density Estimation by Maximum Quantum Entropy

Author:

Publisher:

Published: 1993

Total Pages: 14

ISBN-13:

DOWNLOAD EBOOK

A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets.

Combinatorial Methods in Density Estimation
Combinatorial Methods in Density Estimation

Author: Luc Devroye

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 219

ISBN-13: 1461301254

DOWNLOAD EBOOK

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Combinatorial Methods in Density Estimation
Combinatorial Methods in Density Estimation

Author: Luc Devroye

Publisher: Springer

Published: 2011-04-26

Total Pages: 224

ISBN-13: 9781461301264

DOWNLOAD EBOOK

Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Maximum Entropy and Bayesian Methods Garching, Germany 1998
Maximum Entropy and Bayesian Methods Garching, Germany 1998

Author: Wolfgang von der Linden

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 380

ISBN-13: 9401147108

DOWNLOAD EBOOK

In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory.