Entropy and inference, revisited
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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
LaTex2e, 9 pages, 5 figures; references added, minor revisions introduced, formatting errors corrected