Applications of quantum entropy to statistics
Abstract
This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods.
- Authors:
- Publication Date:
- Research Org.:
- Los Alamos National Lab., NM (United States)
- Sponsoring Org.:
- USDOE, Washington, DC (United States)
- OSTI Identifier:
- 10162539
- Report Number(s):
- LA-UR-94-2168; CONF-9408107-2
ON: DE94014416; TRN: 94:013105
- DOE Contract Number:
- W-7405-ENG-36
- Resource Type:
- Conference
- Resource Relation:
- Conference: American Statistical Association,Toronto (Canada),14-18 Aug 1994; Other Information: PBD: [1994]
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; QUANTUM MECHANICS; IMAGE PROCESSING; STATISTICS; RESPONSE FUNCTIONS; ALGORITHMS; 661300; 661100; OTHER ASPECTS OF PHYSICAL SCIENCE; CLASSICAL AND QUANTUM MECHANICS
Citation Formats
Silver, R N, and Martz, H F. Applications of quantum entropy to statistics. United States: N. p., 1994.
Web.
Silver, R N, & Martz, H F. Applications of quantum entropy to statistics. United States.
Silver, R N, and Martz, H F. 1994.
"Applications of quantum entropy to statistics". United States. https://www.osti.gov/servlets/purl/10162539.
@article{osti_10162539,
title = {Applications of quantum entropy to statistics},
author = {Silver, R N and Martz, H F},
abstractNote = {This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods.},
doi = {},
url = {https://www.osti.gov/biblio/10162539},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jul 01 00:00:00 EDT 1994},
month = {Fri Jul 01 00:00:00 EDT 1994}
}