# Neural Score Matching for High-Dimensional Causal Inference

arXiv: https://arxiv.org/abs/2203.00554 · HTML: https://mlsanity.com/paper/2203.00554/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 51 references that are in the map.
- First posted on arXiv 1 Mar 2022.

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

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Deep Learning for Audio Signal Processing](https://mlsanity.com/paper/1905.00078/) (2019)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference](https://mlsanity.com/paper/1707.06315/) (2017)
- [Matching Using Sufficient Dimension Reduction for Causal Inference](https://mlsanity.com/paper/1702.00444/) (2017)
- [Sufficient Dimension Reduction for Average Causal Effect Estimation](https://mlsanity.com/paper/2009.06444/) (2020)

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

- [A Review of Causality for Learning Algorithms in Medical Image Analysis](https://mlsanity.com/paper/2206.05498/) (2022)
- [Implicitly Guided Design with PropEn: Match your Data to Follow the Gradient](https://mlsanity.com/paper/2405.18075/) (2024)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [C-HDNet: Hyperdimensional Computing for Causal Effect Estimation from Observational Data Under Network Interference](https://mlsanity.com/paper/2501.16562/) (2025)
- [Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation](https://mlsanity.com/paper/2409.05459/) (2024)
- [Causal Transfer in Medical Image Analysis](https://mlsanity.com/paper/2603.24388/) (2026)

## Abstract (arXiv)

Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input dimension grows, and propensity score matching may match highly unrelated units together. To overcome this problem, we develop theoretical results which motivate the use of neural networks to obtain non-trivial, multivariate balancing scores of a chosen level of coarseness, in contrast to the classical, scalar propensity score. We leverage these balancing scores to perform matching for high-dimensional causal inference and call this procedure neural score matching. We show that our method is competitive against other matching approaches on semi-synthetic high-dimensional datasets, both in terms of treatment effect estimation and reducing imbalance.