Matching Using Sufficient Dimension Reduction for Heterogeneity Causal Effect Estimation

TL;DR

This paper introduces a novel matching method using sufficient dimension reduction to effectively estimate causal effects in high-dimensional observational data, addressing the curse of dimensionality and data sufficiency issues.

Contribution

It proves that SDR provides a balance score for confounding adjustment and proposes a non-parametric approach to obtain reduced covariate representations for improved causal inference.

Findings

Outperforms existing matching methods on real-world datasets

Reduces dimensionality while maintaining confounding balance

Effectively balances treatment and control groups

Abstract

Causal inference plays an important role in under standing the underlying mechanisation of the data generation process across various domains. It is challenging to estimate the average causal effect and individual causal effects from observational data with high-dimensional covariates due to the curse of dimension and the problem of data sufficiency. The existing matching methods can not effectively estimate individual causal effect or solve the problem of dimension curse in causal inference. To address this challenge, in this work, we prove that the reduced set by sufficient dimension reduction (SDR) is a balance score for confounding adjustment. Under the theorem, we propose to use an SDR method to obtain a reduced representation set of the original covariates and then the reduced set is used for the matching method. In detail, a non-parametric model is used to learn such a reduced set and to avoid model specification errors. The experimental results on real-world datasets show that the proposed method outperforms the compared matching methods. Moreover, we conduct an experiment analysis and the results demonstrate that the reduced representation is enough to balance the imbalance between the treatment group and control group individuals.