# Matching Using Sufficient Dimension Reduction for Causal Inference

arXiv: https://arxiv.org/abs/1702.00444 · HTML: https://mlsanity.com/paper/1702.00444/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2017.

## Built on by (most cited first, 8 of 8)

- [Neural Score Matching for High-Dimensional Causal Inference](https://mlsanity.com/paper/2203.00554/) (2022)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [Matched Machine Learning: A Generalized Framework for Treatment Effect Inference With Learned Metrics](https://mlsanity.com/paper/2304.01316/) (2023)
- [Estimating treatment effects from single-arm trials via latent-variable modeling](https://mlsanity.com/paper/2311.03002/) (2023)
- [Recovering Latent Confounders from High-dimensional Proxy Variables](https://mlsanity.com/paper/2403.14228/) (2024)
- [Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation](https://mlsanity.com/paper/2409.05459/) (2024)
- [FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows](https://mlsanity.com/paper/2606.01346/) (2026)

## Abstract (arXiv)

To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for matching in the literature, the reduced covariates are estimable nonparametrically under a mild assumption on the original covariates, and are sufficient and effective in imputing the missing potential outcomes. Under the ignorability assumption, the consistency of the proposed approach requires a weaker common support condition. In addition, the researchers are allowed to use different reduced covariates to find matched subjects for different treatment groups. We develop relative asymptotic results, and conduct simulation studies as well as real data analysis to illustrate the usefulness of the proposed approach.