Entropy and Inference, Revisited

We study properties of popular near–uniform (Dirichlet) priors for learn- ing 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. Learning a probability distribution from examples is one of the basic problems in data analysis. Common practical approaches introduce a family of parametric models, leading to questions about model selection.