PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Exact Non-Parametric Bayesian Inference on Infinite Trees
Marcus Hutter
arXiv Number 0903.5342, 2009.

Abstract

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to ``subdivide'', which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, moments, and other quantities. We prove asymptotic convergence and consistency results, and illustrate the behavior of our model on some prototypical functions.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:5848
Deposited By:Marcus Hutter
Deposited On:08 March 2010