Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation

TL;DR

This paper introduces GeoMatching, a novel causal inference method that leverages the intrinsic geometry of data manifolds to improve treatment effect estimation, especially in high-dimensional or noisy settings.

Contribution

GeoMatching learns a low-dimensional Riemannian manifold to incorporate data geometry into matching, enhancing treatment effect estimation over traditional methods.

Findings

GeoMatching outperforms classic matching in synthetic scenarios.

It remains effective with high-dimensional and noisy data.

The method is validated on real-world datasets.

Abstract

Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.