Reproduce “Neural Score Matching for High-Dimensional Causal Inference” on OpenResearch

About this paper

Oscar Clivio, Fabian Falck, Brieuc Lehmann, George Deligiannidis, Chris Holmes

Neural Score Matching, a method that leverages neural networks to generate multivariate balancing scores, is introduced for causal inference in high-dimensional settings. It shows improved Average Treatment Effect (ATT) estimation and covariate balance against traditional approaches on semi-synthetic high-dimensional datasets.

Key insights

• A theoretical framework demonstrates that if a neural network perfectly estimates the propensity score, then each intermediate layer's output is also a balancing score, with subsequent layers forming coarser representations.
• Bounds for imbalance (e.g., Wasserstein distance, MMD) are established, linking the imbalance in lower-dimensional neural scores to the imbalance in the original high-dimensional covariates.
• The framework extends to scenarios where learned scores are not perfect balancing scores, introducing a 'balancing error' term to quantify the deviation from ideal conditions.

Summary by alphaXiv.