# Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors

arXiv: https://arxiv.org/abs/2603.11942 · HTML: https://mlsanity.com/paper/2603.11942/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions](https://mlsanity.com/paper/2303.14226/) (2023)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [TenIPS: Inverse Propensity Sampling for Tensor Completion](https://mlsanity.com/paper/2101.00323/) (2021)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [Generalized Tensor Completion with Non-Random Missingness](https://mlsanity.com/paper/2509.06225/) (2025)
- [Causal Inference on Sequential Treatments via Tensor Completion](https://mlsanity.com/paper/2511.15866/) (2025)

## Abstract (arXiv)

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.