PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Computable Bayesian Compression for Uniformly Discretizable Statistical Models
Lukasz Debowski
In: ALT 2009, Porto, Portugal(2009).

Abstract

Supplementing Vovk and V’yugin’s ‘if’ statement, we show that Bayesian compression provides the best enumerable compression for parameter-typical data if and only if the parameter is Martin-L¨of random with respect to the prior. The result is derived for uniformly discretizable statistical models, introduced here. They feature the crucial property that given a discretized parameter, we can compute how much data is needed to learn its value with little uncertainty. Exponential families and certain nonparametric models are shown to be uniformly discretizable.

EPrint Type:Conference or Workshop Item (Talk)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:6442
Deposited By:Peter Grünwald
Deposited On:08 March 2010