arXiv 12 Jan 2026 · Econometrics
arXiv:2601.07752 · PDF · DOI · OpenAlex · Extracted main text
Estimating the Riesz representer is central to debiased machine learning for causal and structural parameter estimation. We propose generalized Riesz regression, a unified framework for estimating the Riesz representer by fitting a representer model via Bregman divergence minimization. This framework includes various divergences as special cases, such as the squared distance and the Kullback--Leibler (KL) divergence, where the former recovers Riesz regression and the latter recovers tailored loss minimization. Under suitable pairs of divergence and model specifications (link functions), the dual problems of the Riesz representer fitting problem correspond to covariate balancing, which we call automatic covariate balancing. Moreover, under the same specifications, the sample average of outcomes weighted by the estimated Riesz representer satisfies Neyman orthogonality even without estimating the regression function, a property we call automatic Neyman orthogonalization. This property not only reduces the estimation error of Neyman orthogonal scores but also clarifies a key distinction between debiased machine learning and targeted maximum likelihood estimation (TMLE). Our framework can also be viewed as a generalization of density ratio fitting under Bregman divergences to Riesz representer estimation, and it applies beyond density ratio estimation. We provide convergence analyses for both reproducing kernel Hilbert space (RKHS) and neural network model classes. A Python package for generalized Riesz regression is released as genriesz and is available at https://github.com/MasaKat0/genriesz.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| 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 | 0.909 | 8 | 5 | 75% |
| 2 | Masahiro Kato (2025) Nearest neighbor matching as least squares density ratio estimation and riesz regression, 2025c self | 0.894 | 7 | 4 | 71% |
| 3 | Jens Hainmueller (2012) Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies | 0.874 | 9 | 6 | 67% |
| 4 | Masashi Sugiyama, Taiji Suzuki, and Takafumi Kanamori (2012) Density Ratio Estimation in Machine Learning | 0.874 | 9 | 6 | 67% |
| 5 | José R. Zubizarreta (2015) Stable weights that balance covariates for estimation with incomplete outcome data | 0.874 | 6 | 3 | 67% |
| 6 | Masahiro Kato and Takeshi Teshima (2021) Non-negative bregman divergence minimization for deep direct density ratio estimation self | 0.860 | 11 | 8 | 64% |
| 7 | Siming Zheng, Guohao Shen, Yuling Jiao, Yuanyuan Lin, and Jian Huang (2022) An error analysis of deep density-ratio estimation with bregman divergence, 2022 | 0.855 | 8 | 3 | 62% |
| 8 | David Bruns-Smith, Oliver Dukes, Avi Feller, and Elizabeth L Ogburn (2025) Augmented balancing weights as linear regression | 0.851 | 13 | 5 | 62% |
| 9 | B. Rhodes, K. Xu, and M.U. Gutmann (2020) Telescoping density-ratio estimation | 0.843 | 4 | 3 | 75% |
| 10 | van der Laan (2006) Targeted maximum likelihood learning, 2006 | 0.843 | 4 | 3 | 75% |
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