# Sufficient Dimension Reduction for Average Causal Effect Estimation

arXiv: https://arxiv.org/abs/2009.06444 · HTML: https://mlsanity.com/paper/2009.06444/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/2108.03039/) (2021)
- [Neural Score Matching for High-Dimensional Causal Inference](https://mlsanity.com/paper/2203.00554/) (2022)
- [Accurate Use of Label Dependency in Multi-Label Text Classification Through the Lens of Causality](https://mlsanity.com/paper/2310.07588/) (2023)
- [Recovering Latent Confounders from High-dimensional Proxy Variables](https://mlsanity.com/paper/2403.14228/) (2024)
- [An Integrated Causal Inference Framework for Traffic Safety Modeling with Semantic Street-View Visual Features](https://mlsanity.com/paper/2602.13339/) (2026)

## Abstract (arXiv)

Having a large number of covariates can have a negative impact on the quality of causal effect estimation since confounding adjustment becomes unreliable when the number of covariates is large relative to the samples available. Propensity score is a common way to deal with a large covariate set, but the accuracy of propensity score estimation (normally done by logistic regression) is also challenged by large number of covariates. In this paper, we prove that a large covariate set can be reduced to a lower dimensional representation which captures the complete information for adjustment in causal effect estimation. The theoretical result enables effective data-driven algorithms for causal effect estimation. We develop an algorithm which employs a supervised kernel dimension reduction method to search for a lower dimensional representation for the original covariates, and then utilizes nearest neighbor matching in the reduced covariate space to impute the counterfactual outcomes to avoid large-sized covariate set problem. The proposed algorithm is evaluated on two semi-synthetic and three real-world datasets and the results have demonstrated the effectiveness of the algorithm.