# Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression

arXiv: https://arxiv.org/abs/2510.24433 · HTML: https://mlsanity.com/paper/2510.24433/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Off-Policy Evaluation and Learning for External Validity under a Covariate Shift](https://mlsanity.com/paper/2002.11642/) (2020)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)
- [Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.22122/) (2025)
- [Direct Debiased Machine Learning via Bregman Divergence Minimization](https://mlsanity.com/paper/2510.23534/) (2025)

## Built on by (most cited first, 7 of 7)

- [Riesz Regression As Direct Density Ratio Estimation](https://mlsanity.com/paper/2511.04568/) (2025)
- [A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression](https://mlsanity.com/paper/2510.26783/) (2025)
- [Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference](https://mlsanity.com/paper/2511.08303/) (2025)
- [Causal-Policy Forest for End-to-End Policy Learning](https://mlsanity.com/paper/2512.22846/) (2025)
- [genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression](https://mlsanity.com/paper/2602.17543/) (2026)
- [Prediction-Powered Causal Inference by Automatic Debiased Machine Learning and Semi-Supervised Riesz Regression](https://mlsanity.com/paper/2606.12892/) (2026)
- [Vector Search As Nearest Neighbor Matching: RAG-based Policy Learning in Causal Inference](https://mlsanity.com/paper/2607.18225/) (2026)

## Abstract (arXiv)

This study proves that Nearest Neighbor (NN) matching can be interpreted as an instance of Riesz regression for automatic debiased machine learning. Lin et al. (2023) shows that NN matching is an instance of density-ratio estimation with their new density-ratio estimator. Chernozhukov et al. (2024) develops Riesz regression for automatic debiased machine learning, which directly estimates the Riesz representer (or equivalently, the bias-correction term) by minimizing the mean squared error. In this study, we first prove that the density-ratio estimation method proposed in Lin et al. (2023) is essentially equivalent to Least-Squares Importance Fitting (LSIF) proposed in Kanamori et al. (2009) for direct density-ratio estimation. Furthermore, we derive Riesz regression using the LSIF framework. Based on these results, we derive NN matching from Riesz regression. This study is based on our work Kato (2025a) and Kato (2025b).