Causal Matrix Completion

In general, these confounders yield “missing not at random” (MNAR) data, which can severely impact any inference procedure that does not correct for this bias. We develop a formal causal model for matrix completion with MNAR data through the language of potential outcomes, and provide identification arguments for causal estimand of interest. We design a procedure, which we call “synthetic nearest neighbors” (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.

This is based on joint works with Anish Agarwal (MIT), Munther Dahleh (MIT) and Dennis Shen (UC Berkeley).