arXiv 23 Dec 2025 · Econometrics
arXiv:2512.20523 · PDF · DOI · OpenAlex · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Victor Chernozhukov, Whitney K. Newey, Victor Quintas-Martinez, and… (2021) Automatic debiased machine learning via riesz regression, 2021 | 0.894 | 7 | 5 | 71% |
| 2 | Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters | 0.843 | 4 | 4 | 75% |
| 3 | Kristy Choi, Chenlin Meng, Yang Song, and Stefano Ermon (2022) Density ratio estimation via infinitesimal classification | 0.836 | 12 | 6 | 58% |
| 4 | David Bruns-Smith, Oliver Dukes, Avi Feller, and Elizabeth L Ogburn (2025) Augmented balancing weights as linear regression | 0.830 | 7 | 5 | 57% |
| 5 | B. Rhodes, K. Xu, and M.U. Gutmann (2020) Telescoping density-ratio estimation | 0.737 | 5 | 2 | 60% |
| 6 | Takafumi Kanamori, Shohei Hido, and Masashi Sugiyama (2009) A least-squares approach to direct importance estimation | 0.737 | 4 | 3 | 50% |
| 7 | Jiaming Song, Chenlin Meng, and Stefano Ermon (2021) Denoising diffusion implicit models | 0.737 | 3 | 3 | 67% |
| 8 | Pascal Vincent (2011) A connection between score matching and denoising autoencoders | 0.737 | 3 | 3 | 67% |
| 9 | Masahiro Kato (2026) Riesz representer fitting under bregman divergence: A unified framework for debiased machine learning, 2026 self | 0.727 | 13 | 6 | 38% |
| 10 | Kazusato Oko, Shunta Akiyama, and Taiji Suzuki (2023) Diffusion models are minimax optimal distribution estimators | 0.693 | 12 | 4 | 33% |
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