论文标题
估计没有分区功能痛苦的潜力
Estimating a potential without the agony of the partition function
论文作者
论文摘要
估计给定样品的吉布斯密度函数是计算统计和统计学习中的重要问题。尽管通常使用了良好的最大似然法，但它需要计算分区函数（即密度的归一化）。 可以轻松地针对简单的低维问题来计算此功能，但是对于一般密度和高维问题，其计算很困难，甚至是棘手的。在本文中，我们提出了一种基于最大a-posteriori（MAP）估计量的替代方法，我们命名了最大恢复地图（MR-MAP），以得出不需要计算分区函数的估计器，并将问题重新制定为优化问题。我们进一步提出了一种最小动作类型的潜力，使我们能够快速解决优化问题作为馈送屈曲神经网络。我们证明了我们的方法对某些标准数据集的有效性。
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.
