Society for Artificial Intelligence and Statistics
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, and other quantities