Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918384383295488 |
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| author | Luo, Minrui Zhang, Zhiheng |
| author_facet | Luo, Minrui Zhang, Zhiheng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_11942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors Luo, Minrui Zhang, Zhiheng Machine Learning 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. |
| title | Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.11942 |