Generalized Score Matching for General Domains

2020/09/24 by Shiqing Yu, Mathias Drton, Yu, Shiqing +3 · 2 citations
Mathematics · #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #stat.ME #stat.ML

paper · pdf · doi:10.48550/arxiv.2009.11428

50 pages, 14 figures

arxiv created 2020/09/24 · arxiv updated 2020/09/25

Abstract

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 ℝ^m and 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.

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