# Robust Score Matching

arXiv: https://arxiv.org/abs/2501.05105 · HTML: https://mlsanity.com/paper/2501.05105/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Estimation of High-Dimensional Graphical Models Using Regularized Score Matching](https://mlsanity.com/paper/1507.00433/) (2015)
- [Distributed Statistical Estimation and Rates of Convergence in Normal Approximation](https://mlsanity.com/paper/1704.02658/) (2017)
- [Nonparametric graphical model for counts](https://mlsanity.com/paper/1901.00886/) (2019)
- [Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies](https://mlsanity.com/paper/1603.03629/) (2016)

## Built on by (most cited first, 2 of 2)

- [On the distance between mean and geometric median in high dimensions](https://mlsanity.com/paper/2508.12926/) (2025)
- [Euclidean Distance-Based Flow Matching](https://mlsanity.com/paper/2610.18534/) (2026)

## Abstract (arXiv)

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.