LRSVRG-IMC: An SVRG-Based Algorithm for LowRank Inductive Matrix Completion

TL;DR

This paper introduces LRSVRG-IMC, a stochastic variance reduction algorithm for low-rank inductive matrix completion, capable of escaping saddle points and achieving linear convergence with near-optimal sample complexity, validated on synthetic data.

Contribution

The paper proposes a novel SVRG-based algorithm, LRSVRG-IMC, that effectively escapes saddle points and guarantees fast convergence in low-rank IMC problems.

Findings

LRSVRG-IMC achieves linear convergence rate.

The algorithm has near-optimal sample complexity.

Experimental results confirm its effectiveness on synthetic datasets.

Abstract

Low-rank inductive matrix completion (IMC) is currently widely used in IoT data completion, recommendation systems, and so on, as the side information in IMC has demonstrated great potential in reducing sample point remains a major obstacle for the convergence of the nonconvex solutions to IMC. What's more, carefully choosing the initial solution alone does not usually help remove the saddle points. To address this problem, we propose a stocastic variance reduction gradient-based algorithm called LRSVRG-IMC. LRSVRG-IMC can escape from the saddle points under various low-rank and sparse conditions with a properly chosen initial input. We also prove that LRSVVRG-IMC achieves both a linear convergence rate and a near-optimal sample complexity. The superiority and applicability of LRSVRG-IMC are verified via experiments on synthetic datasets.