Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors

TL;DR

This paper introduces MSNN, a novel causal matrix completion method that combines information across multiple treatment levels to improve estimation accuracy in data-scarce scenarios, building on the SNN framework.

Contribution

MSNN extends Synthetic Nearest Neighbors by integrating across treatments, maintaining theoretical guarantees while enhancing data efficiency in causal matrix completion.

Findings

MSNN achieves better estimation accuracy in synthetic datasets.

MSNN outperforms existing methods in real-world data scenarios.

The approach is effective even with limited data per treatment level.

Abstract

Synthetic Nearest Neighbors (SNN) provides a principled solution to causal matrix completion under missing-not-at-random (MNAR) by exploiting local low-rank structure through fully observed anchor submatrices. However, its effectiveness critically relies on sufficient data availability within each treatment level, a condition that often fails in settings with multiple or complex treatments. In this work, we propose Mixed Synthetic Nearest Neighbors (MSNN), a new entry-wise causal identification estimator that integrates information across treatment levels. We show that MSNN retains the finite-sample error bounds and asymptotic normality guarantees of SNN, while enlarging the effective sample size available for estimation. Empirical results on synthetic and real-world datasets illustrate the efficacy of the proposed approach, especially under data-scarce treatment levels.