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A Unified Framework for Debiased Machine Learning: Riesz Representer Fitting under Bregman Divergence

Masahiro Kato

arXiv 12 Jan 2026 · Econometrics

arXiv:2601.07752 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Victor Chernozhukov, Whitney K. Newey, Victor Quintas-Martinez, and… (2021) Automatic debiased machine learning via riesz regression, 20210.9098575%
2Masahiro Kato (2025) Nearest neighbor matching as least squares density ratio estimation and riesz regression, 2025c self0.8947471%
3Jens Hainmueller (2012) Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies0.8749667%
4Masashi Sugiyama, Taiji Suzuki, and Takafumi Kanamori (2012) Density Ratio Estimation in Machine Learning0.8749667%
5José R. Zubizarreta (2015) Stable weights that balance covariates for estimation with incomplete outcome data0.8746367%
6Masahiro Kato and Takeshi Teshima (2021) Non-negative bregman divergence minimization for deep direct density ratio estimation self0.86011864%
7Siming Zheng, Guohao Shen, Yuling Jiao, Yuanyuan Lin, and Jian Huang (2022) An error analysis of deep density-ratio estimation with bregman divergence, 20220.8558362%
8David Bruns-Smith, Oliver Dukes, Avi Feller, and Elizabeth L Ogburn (2025) Augmented balancing weights as linear regression0.85113562%
9B. Rhodes, K. Xu, and M.U. Gutmann (2020) Telescoping density-ratio estimation0.8434375%
10van der Laan (2006) Targeted maximum likelihood learning, 20060.8434375%

Showing the top 10 of 144 scored citations.