Matrix Completion under Interval Uncertainty

TL;DR

This paper introduces an efficient parallel coordinate-descent method for matrix completion under interval uncertainty, demonstrating superior performance in image in-painting and large-scale collaborative filtering tasks.

Contribution

The paper proposes a novel alternating-direction parallel coordinate-descent algorithm tailored for matrix completion with box constraints, improving efficiency and solution quality.

Findings

Outperforms existing methods in image in-painting benchmarks.

Provides high-quality solutions for large-scale collaborative filtering.

Achieves significant speedup, completing 100 million recommendations in 5 minutes.

Abstract

Matrix completion under interval uncertainty can be cast as matrix completion with element-wise box constraints. We present an efficient alternating-direction parallel coordinate-descent method for the problem. We show that the method outperforms any other known method on a benchmark in image in-painting in terms of signal-to-noise ratio, and that it provides high-quality solutions for an instance of collaborative filtering with 100,198,805 recommendations within 5 minutes.