Robust Score Matching

Richard Schwank, Andrew McCormack, Mathias Drton
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1234-1242, 2025.

Abstract

Proposed in Hyv{ä}rinen (2005), score matching is a statistical 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-schwank25a, title = {Robust Score Matching}, author = {Schwank, Richard and McCormack, Andrew and Drton, Mathias}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1234--1242}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/schwank25a/schwank25a.pdf}, url = {https://proceedings.mlr.press/v258/schwank25a.html}, abstract = {Proposed in Hyv{ä}rinen (2005), score matching is a statistical 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.} }
Endnote
%0 Conference Paper %T Robust Score Matching %A Richard Schwank %A Andrew McCormack %A Mathias Drton %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-schwank25a %I PMLR %P 1234--1242 %U https://proceedings.mlr.press/v258/schwank25a.html %V 258 %X Proposed in Hyv{ä}rinen (2005), score matching is a statistical 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.
APA
Schwank, R., McCormack, A. & Drton, M.. (2025). Robust Score Matching. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1234-1242 Available from https://proceedings.mlr.press/v258/schwank25a.html.

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