Generalized Score Matching for General Domains
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 $\mathbb{R}^m$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.11428
- arXiv:
- arXiv:2009.11428
- Bibcode:
- 2020arXiv200911428Y
- Keywords:
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- Statistics - Methodology;
- Statistics - Machine Learning
- E-Print:
- 50 pages, 14 figures