Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors
This work addresses a bottleneck in causal inference for settings with complex treatments, offering an incremental improvement over prior methods.
The paper tackled the problem of causal matrix completion under missing-not-at-random data with multiple treatments, where existing methods fail due to insufficient data per treatment level, and proposed Mixed Synthetic Nearest Neighbors (MSNN) to integrate information across treatments, achieving improved performance especially in data-scarce settings.
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.