Likelihood-Free Inference via Structured Score Matching

Haoyu Jiang, Yuexi Wang, Yun Yang
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1567-1575, 2026.

Abstract

In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We develop a likelihood-free inference framework that combines score matching with gradient-based optimization and bootstrap procedures to facilitate parameter estimation together with uncertainty quantification. The proposed methodology introduces tailored score-matching estimators for approximating likelihood score functions, and incorporates an architectural regularization scheme that embeds the statistical structure of log-likelihood scores to improve both accuracy and scalability. We provide theoretical guarantees and demonstrate the practical utility of the method through simulations and benchmark applications, where it performs favorably compared to existing approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-jiang26b, title = { Likelihood-Free Inference via Structured Score Matching }, author = {Jiang, Haoyu and Wang, Yuexi and Yang, Yun}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1567--1575}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/jiang26b/jiang26b.pdf}, url = {https://proceedings.mlr.press/v300/jiang26b.html}, abstract = { In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We develop a likelihood-free inference framework that combines score matching with gradient-based optimization and bootstrap procedures to facilitate parameter estimation together with uncertainty quantification. The proposed methodology introduces tailored score-matching estimators for approximating likelihood score functions, and incorporates an architectural regularization scheme that embeds the statistical structure of log-likelihood scores to improve both accuracy and scalability. We provide theoretical guarantees and demonstrate the practical utility of the method through simulations and benchmark applications, where it performs favorably compared to existing approaches. } }
Endnote
%0 Conference Paper %T Likelihood-Free Inference via Structured Score Matching %A Haoyu Jiang %A Yuexi Wang %A Yun Yang %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-jiang26b %I PMLR %P 1567--1575 %U https://proceedings.mlr.press/v300/jiang26b.html %V 300 %X In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We develop a likelihood-free inference framework that combines score matching with gradient-based optimization and bootstrap procedures to facilitate parameter estimation together with uncertainty quantification. The proposed methodology introduces tailored score-matching estimators for approximating likelihood score functions, and incorporates an architectural regularization scheme that embeds the statistical structure of log-likelihood scores to improve both accuracy and scalability. We provide theoretical guarantees and demonstrate the practical utility of the method through simulations and benchmark applications, where it performs favorably compared to existing approaches.
APA
Jiang, H., Wang, Y. & Yang, Y.. (2026). Likelihood-Free Inference via Structured Score Matching . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1567-1575 Available from https://proceedings.mlr.press/v300/jiang26b.html.

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