Density estimation by maximum quantum entropy
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.
- 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:
- 10193649
- Report Number(s):
- LA-UR-93-3550; CONF-9308188-1; ON: DE94002626; TRN: 93:025696
- Resource Relation:
- Conference: Maximum entropy and Bayesian methods `93,Santa Barbara, CA (United States),1-4 Aug 1993; Other Information: PBD: [1993]
- Country of Publication:
- United States
- Language:
- English
Similar Records
Applications of quantum entropy to statistics
Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers