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.

翻译：给定样本估计吉布斯密度函数是计算统计学与统计学习中的重要问题。尽管广泛使用的最大似然方法常被采用，但其需要计算配分函数（即密度归一化）。该函数在简单低维问题中易于计算，但对于一般密度及高维问题，其计算困难甚至难以处理。本文提出一种基于最大后验（MAP）估计器的替代方法，命名为最大恢复MAP（MR-MAP），以构建无需计算配分函数的估计器，并将问题重构为优化问题。我们进一步提出一种最小作用量型势能，通过前馈双曲神经网络快速求解该优化问题。在若干标准数据集上的实验验证了所提方法的有效性。