不受配分函数影响的势函数估计
Estimating a potential without the agony of the partition function
摘要：
给定样本的吉布斯密度函数的估计是计算统计和统计学习中的一个重要问题。尽管通常使用已建立的最大似然方法，但其需要计算配分函数（即，密度的归一化）。对于简单的低维问题，该函数可以很容易地计算，但对于一般密度和高维问题，它的计算是困难的，甚至是棘手的。在本文中，我们提出了一种替代方法的基础上最大后验概率（MAP）估计，我们命名为最大恢复MAP（MR-MAP），得到估计，不需要计算的分区函数，并重新制定的问题作为一个优化问题。我们进一步提出了一个最小动作类型的潜力，使我们能够快速解决前馈双曲神经网络的优化问题。我们证明了我们的方法在一些标准数据集上的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
