Yu Shiqing, Drton Mathias, Shojaie Ali
Department of Statistics, University of Washington, Seattle, WA, U.S.A.
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark; Department of Statistics, University of Washington, Seattle, WA, U.S.A.
J Mach Learn Res. 2019 Apr;20.
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over . Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant, . In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. As an example, we consider a general class of pairwise interaction models. Addressing an overlooked inexistence problem, we generalize the regularized score matching method of Lin et al. (2016) and improve its theoretical guarantees for non-negative Gaussian graphical models.
在估计概率密度函数的参数时，一个常见的挑战是归一化常数的难以处理性。在这种情况下，虽然可以使用数值积分来实现最大似然估计，但该方法在计算上变得很密集。Hyvärinen（2005）的得分匹配方法避免了直接计算归一化常数，并为 上的连续分布的指数族产生了封闭形式的估计。Hyvärinen（2007）将该方法扩展到了非负象限 上支持的分布。在本文中，我们给出了一种针对非负数据的得分匹配的广义形式，它提高了估计效率。作为一个例子，我们考虑一类一般的成对相互作用模型。针对一个被忽视的不存在问题，我们推广了Lin等人（2016）的正则化得分匹配方法，并改进了其对非负高斯图形模型的理论保证。
