Representational Transfer Learning for Matrix Completion
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.
Cite
@article{arxiv.2412.06233,
title = {Representational Transfer Learning for Matrix Completion},
author = {Yong He and Zeyu Li and Dong Liu and Kangxiang Qin and Jiahui Xie},
journal= {arXiv preprint arXiv:2412.06233},
year = {2024}
}