Likelihood-Free Inference via Structured Score Matching

TL;DR

This paper introduces a likelihood-free inference method combining score matching, gradient optimization, and bootstrap techniques to estimate parameters and quantify uncertainty in complex models with intractable likelihoods.

Contribution

It develops a novel score-matching based framework with regularization for scalable, accurate likelihood-free inference and uncertainty quantification.

Findings

Method performs favorably compared to existing approaches.

Provides theoretical guarantees for the proposed estimators.

Demonstrates practical utility through numerical experiments.

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.