Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation
This work addresses a domain-specific problem in causal inference for researchers and practitioners, offering an incremental improvement by incorporating geometric considerations into matching methods.
The paper tackled the problem of estimating treatment effects in causal inference by addressing the limitations of classic matching methods that ignore data geometry and struggle with high-dimensional noisy covariates, proposing GeoMatching which learns a latent Riemannian manifold for matching and yields more effective estimators as dimensionality increases or in the presence of outliers.
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.