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Title: Quantum statistical inference for density estimation

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Los Alamos National Lab., NM (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10193654
Report Number(s):
LA-UR-93-3552; CONF-9308107-4
ON: DE94002625
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: Joint American Statistical Association (ASA), Institute of Mathematics Statistics and Biometric Society conference,San Francisco, CA (United States),8-12 Aug 1993; Other Information: PBD: [1993]
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; STATISTICAL MODELS; STATISTICS; ENTROPY; STATISTICAL MECHANICS; RESPONSE FUNCTIONS; PARAMETRIC ANALYSIS; 990200; 661300; MATHEMATICS AND COMPUTERS; OTHER ASPECTS OF PHYSICAL SCIENCE

Citation Formats

Silver, R N, Martz, H F, and Wallstrom, T. Quantum statistical inference for density estimation. United States: N. p., 1993. Web.
Silver, R N, Martz, H F, & Wallstrom, T. Quantum statistical inference for density estimation. United States.
Silver, R N, Martz, H F, and Wallstrom, T. Mon . "Quantum statistical inference for density estimation". United States. https://www.osti.gov/servlets/purl/10193654.
@article{osti_10193654,
title = {Quantum statistical inference for density estimation},
author = {Silver, R N and Martz, H F and Wallstrom, T},
abstractNote = {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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1993},
month = {11}
}

Conference:
Other availability
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