Exploiting Observation Bias to Improve Matrix Completion

We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma and Chen. Instead of treating this observation bias as a disadvantage, as is typically the case, our goal is to exploit the shared information between the bias and the outcome of interest to improve predictions. Towards this, we propose a simple two-stage algorithm: (i) interpreting the observation pattern as a fully observed noisy matrix, we apply traditional matrix completion methods to the observation pattern to estimate the distances between the latent factors; (ii) we apply supervised learning on the recovered features to impute missing observations. We establish finite-sample error rates that are competitive with the corresponding supervised learning parametric rates, suggesting that our learning performance is comparable to having access to the unobserved covariates. Empirical evaluation using a real-world dataset reflects similar performance gains, with our algorithm's estimates having 30x smaller mean squared error compared to traditional matrix completion methods.