ScoreMatchingRiesz: Score Matching for Debiased Machine Learning and Policy Path Estimation

TL;DR

ScoreMatchingRiesz introduces a novel score matching approach for estimating Riesz representers, improving debiased machine learning and policy effect estimation through stable, efficient methods and a new policy path concept.

Contribution

The paper develops ScoreMatchingRiesz, a new estimator for Riesz representers using score matching, enabling more stable and efficient causal and policy effect estimation.

Findings

Achieves $ oot{n}$-consistency and asymptotic efficiency in estimation.

Introduces the policy path for better interpretability of policy effects.

Leverages denoising score matching and density ratio estimation techniques.

Abstract

We propose ScoreMatchingRiesz, a family of Riesz representer estimators based on score matching. The Riesz representer is a key nuisance component in debiased machine learning, enabling $\sqrt{n}$-consistent and asymptotically efficient estimation of causal and structural targets via Neyman-orthogonal scores. We formulate Riesz representer estimation as a score estimation problem. This perspective stabilizes representer estimation by allowing us to leverage denoising score matching and telescoping density ratio estimation. We also introduce the policy path, a parameter that captures how policy effects evolve under continuous treatments. We show that the policy path can be estimated via score matching by smoothly connecting average marginal effect (AME) and average policy effect (APE) estimation, which improves the interpretability of policy effects.