Finite Sample Bounds for Learning with Score Matching

TL;DR

This paper provides the first non-asymptotic sample complexity bounds for learning exponential family distributions with score matching, showing polynomial dependence on model dimension.

Contribution

It offers the first non-asymptotic analysis of score matching for exponential families, filling a gap in theoretical understanding.

Findings

Derived polynomial sample bounds for exponential family learning

First non-asymptotic bounds established for score matching

Results applicable to high-dimensional polynomial exponential families

Abstract

Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics. In recent years, score matching has become a widely used method for learning exponential families with continuous variables due to its computational ease when compared against maximum likelihood estimation. However, theoretical understanding of the statistical properties of score matching is still lacking. In this work, we provide a non-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching. The derived sample bounds show a polynomial dependence on the model dimension. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity.