High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching

Daniel James Williams, Leyang Wang, Qizhen Ying, Song Liu, Mladen Kolar
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3493-3501, 2025.

Abstract

This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time and estimating changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets. The code reproducing our experiments can be found at: \url{https://github.com/Leyangw/tsm}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-williams25a, title = {High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching}, author = {Williams, Daniel James and Wang, Leyang and Ying, Qizhen and Liu, Song and Kolar, Mladen}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3493--3501}, 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/williams25a/williams25a.pdf}, url = {https://proceedings.mlr.press/v258/williams25a.html}, abstract = {This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time and estimating changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets. The code reproducing our experiments can be found at: \url{https://github.com/Leyangw/tsm}.} }
Endnote
%0 Conference Paper %T High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching %A Daniel James Williams %A Leyang Wang %A Qizhen Ying %A Song Liu %A Mladen Kolar %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-williams25a %I PMLR %P 3493--3501 %U https://proceedings.mlr.press/v258/williams25a.html %V 258 %X This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time and estimating changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets. The code reproducing our experiments can be found at: \url{https://github.com/Leyangw/tsm}.
APA
Williams, D.J., Wang, L., Ying, Q., Liu, S. & Kolar, M.. (2025). High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3493-3501 Available from https://proceedings.mlr.press/v258/williams25a.html.

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