Robust Score Matching

TL;DR

This paper introduces a robust score matching method using the geometric median of means, providing consistent parameter estimates in contaminated data scenarios while maintaining convexity in exponential family models.

Contribution

It develops a robust score matching procedure that is resilient to data contamination and retains convexity in exponential family models, enabling support recovery guarantees.

Findings

Performs comparably to standard score matching without contamination

Outperforms standard methods with contaminated data

Supports recovery in exponential family graphical models

Abstract

Proposed in Hyv\"arinen (2005), score matching is a parameter estimation procedure that does not require computation of distributional normalizing constants. In this work we utilize the geometric median of means to develop a robust score matching procedure that yields consistent parameter estimates in settings where the observed data has been contaminated. A special appeal of the proposed method is that it retains convexity in exponential family models. The new method is therefore particularly attractive for non-Gaussian, exponential family graphical models where evaluation of normalizing constants is intractable. Support recovery guarantees for such models when contamination is present are provided. Additionally, support recovery is studied in numerical experiments and on a precipitation dataset. We demonstrate that the proposed robust score matching estimator performs comparably to the standard score matching estimator when no contamination is present but greatly outperforms this estimator in a setting with contamination.