Quantum statistical inference for density estimation
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.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10193654
- Report Number(s):
- LA-UR-93-3552; CONF-9308107-4; ON: DE94002625
- 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
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Related Subjects
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