  Maximum entropy (MAXENT) method has a large number of applications in
theoretical and applied machine learning, since it provides a convenient
non-parametric tool for estimating unknown probabilities. The method is a major
contribution of statistical physics to probabilistic inference. However, a
systematic approach towards its validity limits is currently missing. Here we
study MAXENT in a Bayesian decision theory set-up, i.e. assuming that there
exists a well-defined prior Dirichlet density for unknown probabilities, and
that the average Kullback-Leibler (KL) distance can be employed for deciding on
the quality and applicability of various estimators. These allow to evaluate
the relevance of various MAXENT constraints, check its general applicability,
and compare MAXENT with estimators having various degrees of dependence on the
prior, viz. the regularized maximum likelihood (ML) and the Bayesian
estimators. We show that MAXENT applies in sparse data regimes, but needs
specific types of prior information. In particular, MAXENT can outperform the
optimally regularized ML provided that there are prior rank correlations
between the estimated random quantity and its probabilities.
