@inproceedings{
li2024a,
title={A Pairwise Pseudo-likelihood Approach for Matrix Completion with Informative Missingness},
author={Jiangyuan Li and Jiayi Wang and Raymond K. W. Wong and Kwun Chuen Gary Chan},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=ZGN8dOhpi6}
}
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.
A Pairwise Pseudo-likelihood Approach for Matrix Completion with Informative Missingness
Jiangyuan Li Jiayi Wang Raymond K. W. Wong Kwun Chuen Gary Chan