  Estimating a Gibbs density function given a sample is an important problem in
computational statistics and statistical learning. Although the well
established maximum likelihood method is commonly used, it requires the
computation of the partition function (i.e., the normalization of the density).
  This function can be easily calculated for simple low-dimensional problems
but its computation is difficult or even intractable for general densities and
high-dimensional problems. In this paper we propose an alternative approach
based on Maximum A-Posteriori (MAP) estimators, we name Maximum Recovery MAP
(MR-MAP), to derive estimators that do not require the computation of the
partition function, and reformulate the problem as an optimization problem. We
further propose a least-action type potential that allows us to quickly solve
the optimization problem as a feed-forward hyperbolic neural network. We
demonstrate the effectiveness of our methods on some standard data sets.
