A note on the statistical view of matrix completion

TL;DR

This paper offers a statistical perspective on matrix completion, showing it remains valid even without the common MCAR assumption, thus broadening its theoretical foundation.

Contribution

It introduces a simple statistical interpretation of matrix completion that relaxes the need for the MCAR assumption, expanding the understanding of its validity.

Findings

Matrix completion can be justified through statistical models.

It remains valid without the missing completely at random assumption.

Provides a new perspective linking matrix completion to missing data analysis.

Abstract

A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and principled estimation procedure even without the missing completely at random (MCAR) assumption, which almost all of the current theoretical studies of matrix completion assume.