Generalized Score Matching for General Domains
This work addresses density estimation for data restricted to subsets of real space, which is incremental as it extends existing score matching methods to more general domains.
The authors tackled the problem of estimating density functions on general domains with intractable normalizing constants by generalizing score matching to accommodate a broad class of domains, applying it to truncated graphical and pairwise interaction models with theoretical guarantees and empirical advantages.
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.