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. In Bayesian inference one assigns 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...[Show more]
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