Exact non-parametric Bayesian inference on infinite trees
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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