Likelihood-Free Inference via Structured Score Matching

2026-03-30

AI Summary

This work addresses the challenge of parameter inference and uncertainty quantification in generative models where the likelihood function is intractable. We propose a likelihood-free inference framework that approximates the gradient of the log-likelihood via structured score matching, enabling efficient estimation through gradient-based optimization combined with bootstrap resampling. The key innovation lies in a regularized neural network architecture that embeds statistical structure and a tailored score matching estimator, which together ensure theoretical convergence while substantially improving estimation accuracy and scalability. Numerical experiments demonstrate that the proposed method outperforms existing approaches in both parameter estimation accuracy and the reliability of uncertainty quantification.

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 numerical experiments, where it performs favorably compared to existing approaches.

Problem

• likelihood-free inference
• score matching
• generative models
• parameter estimation
• intractable likelihood

Innovation

• likelihood-free inference
• score matching
• structured regularization
• uncertainty quantification
• gradient-based optimization