Representational Transfer Learning for Matrix Completion

Yong He; Zeyu Li; Dong Liu; Kangxiang Qin; Jiahui Xie

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arXiv · 2412.06233

Representational Transfer Learning for Matrix Completion

Yong He·Zeyu Li·Dong Liu·Kangxiang Qin·Jiahui Xie

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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.

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BibTeX RIS

Yong He, Zeyu Li, Dong Liu, Kangxiang Qin, Jiahui Xie. 2024-12-09. Representational Transfer Learning for Matrix Completion. https://arxiv.org/abs/2412.06233

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