Representational Transfer Learning for Matrix Completion

TL;DR

This paper introduces a transfer learning approach for matrix completion that leverages multiple source representations to improve estimation accuracy, using a novel framework based on singular subspace aggregation and low-dimensional regression.

Contribution

It presents a new representational transfer learning framework for matrix completion that integrates source information via singular subspace analysis and transforms the problem into a low-dimensional regression.

Findings

Enhanced matrix completion accuracy demonstrated through simulations.

Robustness against negative transfer shown in real data experiments.

Statistical efficiency guaranteed by the proposed method.

Abstract

We propose to transfer representational knowledge from multiple sources to a target noisy matrix completion task by aggregating singular subspaces information. Under our representational similarity framework, we first integrate linear representation information by solving a two-way principal component analysis problem based on a properly debiased matrix-valued dataset. After acquiring better column and row representation estimators from the sources, the original high-dimensional target matrix completion problem is then transformed into a low-dimensional linear regression, of which the statistical efficiency is guaranteed. A variety of extensional arguments, including post-transfer statistical inference and robustness against negative transfer, are also discussed alongside. Finally, extensive simulation results and a number of real data cases are reported to support our claims.