Transfer Learning for Matrix Completion

TL;DR

This paper introduces a transfer learning approach for matrix completion that leverages auxiliary data to improve estimation, with proven optimality and a method to identify relevant sources, validated through simulations and real data.

Contribution

It proposes a novel transfer learning procedure for matrix completion, including source relevance detection, with theoretical guarantees and practical validation.

Findings

Out method outperforms traditional single-target methods when source matrices are close to the target.

The approach achieves minimax optimal convergence rates by leveraging advanced concentration inequalities.

A new detection procedure effectively identifies informative sources, ensuring reliable transfer learning.

Abstract

In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank target matrix with auxiliary data available. We propose a transfer learning procedure given prior information on which source datasets are favorable. We study its convergence rates and prove its minimax optimality. Our analysis reveals that with the source matrices close enough to the target matrix, out method outperforms the traditional method using the single target data. In particular, we leverage the advanced sharp concentration inequalities introduced in \cite{brailovskaya2024universality} to eliminate a logarithmic factor in the convergence rate, which is crucial for proving the minimax optimality. When the relevance of source datasets is unknown, we develop an efficient detection procedure to identify informative sources and establish its selection consistency. Simulations and real data analysis are conducted to support the validity of our methodology.