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

arXiv: https://arxiv.org/abs/2409.05459 · HTML: https://mlsanity.com/paper/2409.05459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 16 of 16)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Metrics for Deep Generative Models](https://mlsanity.com/paper/1711.01204/) (2017)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference](https://mlsanity.com/paper/1707.06315/) (2017)
- [Probabilistic ODE Solutions in Millions of Dimensions](https://mlsanity.com/paper/2110.11812/) (2021)
- [A prior-based approximate latent Riemannian metric](https://mlsanity.com/paper/2103.05290/) (2021)
- [Policy Learning with Asymmetric Counterfactual Utilities](https://mlsanity.com/paper/2206.10479/) (2022)
- [Matching Using Sufficient Dimension Reduction for Causal Inference](https://mlsanity.com/paper/1702.00444/) (2017)
- [Neural Score Matching for High-Dimensional Causal Inference](https://mlsanity.com/paper/2203.00554/) (2022)
- [Doing Great at Estimating CATE? On the Neglected Assumptions in Benchmark Comparisons of Treatment Effect Estimators](https://mlsanity.com/paper/2107.13346/) (2021)
- [Cautionary Tales on Synthetic Controls in Survival Analyses](https://mlsanity.com/paper/2312.00501/) (2023)
- [Matching Using Sufficient Dimension Reduction for Heterogeneity Causal Effect Estimation](https://mlsanity.com/paper/2301.01549/) (2023)

## Abstract (arXiv)

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.