COMPOUND BAYES LEARNING WITHOUT A TEACHER.
Abstract
The compound decision problem and the empirical Bayes problem are considered. The underlying probability densities of the unlabeled samples are specified as belonging only to a family of probability density functions. Under assumptions of identifiability and some regularity conditions, the unknown probability density functions and the frequencies of the samples are estimated from the received samples. Based on these estimates, a compound decision procedure is exhibited such that the upper bound of the difference between the risk corresponding to the compound rule and the component Bayes risk on the empirical prior probabilities converges to zero. Rates of convergence of the upper bound to zero are given for the empirical Bayes problem. In the empirical Bayes problem a nonparametric estimation is considered and, under certain assumptions, a decision rule is exhibited such that the corresponding risk converges to the optimal Bayes risk. Rates of convergence are given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0822907
Entities
People
- Normonds Alens
Organizations
- Stanford University