Generalized score matching for general domains.

Abstract

Estimation of density functions supported on general domains arises when the data are 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 [Formula: see text] and [Formula: see text]. 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.