论文标题
通用域的广义分数匹配
Generalized Score Matching for General Domains
论文作者
论文摘要
当数据自然限制为真实空间的适当子集时，就会出现在通用域上支持的密度函数的估计。这个问题通常通过棘手的归一化常量而复杂。得分匹配提供了一种强大的工具，用于估计具有如此棘手的归一化常数的密度，但是最初提出的限于$ \ Mathbb {r}^m $和$ \ Mathbb {r} _+^m $上的密度。在本文中，我们提供了分数匹配的自然概括，可容纳在非常一般的域上支持的密度。我们将框架应用于截短的图形和成对相互作用模型，并为所得估计器提供理论保证。我们还将最近提出的方法从界限到无限域中概括，并从经验上证明了我们方法的优势。
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching provides a powerful tool for estimating densities with such intractable normalizing constants, but as originally proposed is limited to densities on $\mathbb{R}^m$ and $\mathbb{R}_+^m$. In this paper, we offer a natural generalization of score matching that accommodates densities supported on a very general class of domains. We apply the framework to truncated graphical and pairwise interaction models, and provide theoretical guarantees for the resulting estimators. We also generalize a recently proposed method from bounded to unbounded domains, and empirically demonstrate the advantages of our method.
