Riesz Regression As Direct Density Ratio Estimation

• URL: http://arxiv.org/abs/2511.04568v1
• Date: Thu, 06 Nov 2025 17:25:05 GMT
• Title: Riesz Regression As Direct Density Ratio Estimation
• Authors: Masahiro Kato,
• Abstract summary: This study shows that Riesz regression is closely related to direct density-ratio estimation (DRE) in important cases.<n>Specifically, the idea and objective in Riesz regression coincide with the one in least-squares importance fitting in DRE estimation.
• Score: 6.44705221140412
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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