Matrix Completion for Structured Observations

TL;DR

This paper introduces a modified matrix completion method that accounts for structural differences between observed and missing data, improving prediction accuracy in applications like user ratings where missingness indicates disinterest.

Contribution

It proposes a regularized nuclear norm minimization approach that incorporates structural information about missing entries, enhancing matrix completion performance.

Findings

Outperforms standard nuclear norm minimization in certain scenarios

Effectively models structural differences between observed and missing data

Applicable to real-world problems like recommendation systems

Abstract

The need to predict or fill-in missing data, often referred to as matrix completion, is a common challenge in today's data-driven world. Previous strategies typically assume that no structural difference between observed and missing entries exists. Unfortunately, this assumption is woefully unrealistic in many applications. For example, in the classic Netflix challenge, in which one hopes to predict user-movie ratings for unseen films, the fact that the viewer has not watched a given movie may indicate a lack of interest in that movie, thus suggesting a lower rating than otherwise expected. We propose adjusting the standard nuclear norm minimization strategy for matrix completion to account for such structural differences between observed and unobserved entries by regularizing the values of the unobserved entries. We show that the proposed method outperforms nuclear norm minimization in certain settings.