A Pairwise Pseudo-likelihood Approach for Matrix Completion with Informative Missingness

Jiangyuan Li, Jiayi Wang, Raymond K. W. Wong, Kwun Chuen Gary Chan

Keywords: Identifiability; missing not at random; U-statistics

Abstract: While several recent matrix completion methods are developed to deal with non-uniform observation probabilities across matrix entries, very few allow the missingness to depend on the mostly unobserved matrix measurements, which is generally ill-posed. We aim to tackle a subclass of these ill-posed settings, characterized by a flexible separable observation probability assumption that can depend on the matrix measurements. We propose a regularized pairwise pseudo-likelihood approach for matrix completion and prove that the proposed estimator can asymptotically recover the low-rank parameter matrix up to an identifiable equivalence class of a constant shift and scaling, at a near-optimal asymptotic convergence rate of the standard well-posed (non-informative missing) setting, while effectively mitigating the impact of informative missingness. The efficacy of our method is validated via numerical experiments, positioning it as a robust tool for matrix completion to mitigate data bias.

Primary Area: Other (please use sparingly, only use the keyword field for more details)

Submission Number: 14957