# Interpretable Matrix Completion: A Discrete Optimization Approach

## TL;DR

This paper introduces Interpretable Matrix Completion, a novel approach that uses side information and a binary convex optimization reformulation to provide meaningful insights into low-rank matrices, scalable to very large sizes.

## Contribution

It presents OptComplete, a scalable algorithm based on stochastic cutting planes for interpretable matrix completion, with demonstrated efficiency and accuracy on large datasets.

## Key findings

- OptComplete scales efficiently to matrices of size 10^6 by 10^6.
- The method achieves competitive accuracy compared to state-of-the-art techniques.
- It provides interpretability by revealing factors influencing the matrix.

## Abstract

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be reformulated as a binary convex optimization problem. We design OptComplete, based on a novel concept of stochastic cutting planes to enable efficient scaling of the algorithm up to matrices of sizes $n=10^6$ and $m=10^6$. We report experiments on both synthetic and real-world datasets that show that OptComplete has favorable scaling behavior and accuracy when compared with state-of-the-art methods for other types of matrix completion, while providing insight on the factors that affect the matrix.