Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors

Minrui Luo; Zhiheng Zhang

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arXiv · 2603.11942

Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors

Minrui Luo·Zhiheng Zhang

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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.

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Minrui Luo, Zhiheng Zhang. 2026-03-12. Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors. https://arxiv.org/abs/2603.11942

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