Representational Transfer Learning for Matrix Completion

• URL: http://arxiv.org/abs/2412.06233v1
• Date: Mon, 09 Dec 2024 06:14:47 GMT
• Title: Representational Transfer Learning for Matrix Completion
• Authors: Yong He, Zeyu Li, Dong Liu, Kangxiang Qin, Jiahui Xie,
• Abstract summary: 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. The original high-dimensional target matrix completion problem is then transformed into a low-dimensional linear regression.
• Score: 11.089932151845916
• License:
• 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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