Entropy and inference, revisited

Abstract

We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument expands the priors into their infinite mixture and resolves most of the observed problems. This leads to a surprisingly good estimator of entropies of discrete distributions.

LaTex2e, 9 pages, 5 figures; references added, minor revisions introduced, formatting errors corrected