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

We propose \emph{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. The replication code is available in the genriesz library.

Economists and policymakers often ask “what if” questions, such as how financial markets would change if a central bank made a different interest-rate move. Debiased machine learning (DML) and automatic debiased machine learning use modern machine learning to estimate such effects, but their estimators rely on a bias-correction term, the Riesz representer, whose estimation can be unstable in high dimensions. We introduce ScoreMatchingRiesz, a more stable way to estimate this correction term. The key idea is to adapt score matching, also used in diffusion models for image generation, to causal estimation. For comparisons between policy scenarios, the method connects scenarios by a smooth path and integrates scores along it, avoiding direct endpoint-to-endpoint density ratio estimation. Building on Kato (2026), “A Unified Framework for Debiased Machine Learning: Riesz Representer Fitting under Bregman Divergence,” we also relate the method to generalized Riesz regression (Bregman-Riesz regression) and covariate balancing. We propose the policy path, which traces a curve showing how an effect changes as the policy shift grows, rather than reporting one number. We demonstrate these ideas using data on monetary policy and equity returns, giving economists a more stable and informative way to study policy impacts.