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Riesz Regression As Direct Density Ratio Estimation

Masahiro Kato

arXiv 6 Nov 2025 · Statistics — Machine Learning

arXiv:2511.04568 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Riesz regression has garnered attention as a tool in debiased machine learning for causal and structural parameter estimation (Chernozhukov et al., 2021). This study shows that Riesz regression is closely related to direct density-ratio estimation (DRE) in important cases, including average treat- ment effect (ATE) estimation. Specifically, the idea and objective in Riesz regression coincide with the one in least-squares importance fitting (LSIF, Kanamori et al., 2009) in direct density-ratio estimation. While Riesz regression is general in the sense that it can be applied to Riesz representer estimation in a wide class of problems, the equivalence with DRE allows us to directly import exist- ing results in specific cases, including convergence-rate analyses, the selection of loss functions via Bregman-divergence minimization, and regularization techniques for flexible models, such as neural networks. Conversely, insights about the Riesz representer in debiased machine learning broaden the applications of direct density-ratio estimation methods. This paper consolidates our prior results in Kato (2025a) and Kato (2025b).

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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, 20211.00054100%
2Masahiro Kato and Takeshi Teshima (2021) Non-negative bregman divergence minimization for deep direct density ratio estimation self0.73732100%
3Masahiro Kato (2025) Direct bias-correction term estimation for propensity scores and average treatment effect estimation, 2025a self0.73732100%
4Masahiro Kato (2026) A unified framework for debiased machine learning: Riesz representer fitting under bregman divergence, 2026 self0.73732100%
5Masashi Sugiyama, Taiji Suzuki, and Takafumi Kanamori (2011) Density ratio matching under the bregman divergence: A unified framework of density ratio estimation0.73732100%
6Jens Hainmueller (2012) Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies0.64422100%
7Takafumi Kanamori, Shohei Hido, and Masashi Sugiyama (2009) A least-squares approach to direct importance estimation0.64422100%
8Takafumi Kanamori, Taiji Suzuki, and Masashi Sugiyama (2012) Statistical analysis of kernel-based least-squares density-ratio estimation0.64422100%
9Masahiro Kato (2025) Nearest neighbor matching as least squares density ratio estimation and riesz regression, 2025b self0.64422100%
10Zhexiao Lin, Peng Ding, and Fang Han (2023) Estimation based on nearest neighbor matching: from density ratio to average treatment effect0.64422100%

Showing the top 10 of 30 scored citations.