Simulation-based Inference via Structured Score Matching

YUEXI WANG – UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN

ABSTRACT

Simulation-based inference (SBI) provides a powerful framework for statistical analysis when the likelihood function is intractable but simulations are available. I will present a unified framework that leverages structured score matching to enable both maximum likelihood estimation and Bayesian posterior sampling in such likelihood-free settings. The key idea is to approximate the intractable likelihood score function with neural networks that embed the statistical structures of likelihood score through architectural regularization. These structural constraints enhance estimation accuracy, scalability, and uncertainty quantification. We establish theoretical guarantees for the proposed methods and demonstrate their practical advantages on benchmark tasks and challenging high-dimensional problems, where they perform favorably against existing approaches.

RELATED PAPERS:

• Jiang, H., Wang, Y. and Yang, Y. (2025). Simulation-based Inference via Langevin Dynamics with Score Matching. https://arxiv.org/abs/2509.03853
• Jiang, H., Wang, Y. and Yang, Y. (2025). Likelihood-Free Inference via Structured Score Matching. (Manuscript available upon request)