Representational Transfer Learning for Matrix Completion
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912149307129856 |
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| author | He, Yong Li, Zeyu Liu, Dong Qin, Kangxiang Xie, Jiahui |
| author_facet | He, Yong Li, Zeyu Liu, Dong Qin, Kangxiang Xie, Jiahui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representational Transfer Learning for Matrix Completion He, Yong Li, Zeyu Liu, Dong Qin, Kangxiang Xie, Jiahui Machine Learning 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. |
| title | Representational Transfer Learning for Matrix Completion |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2412.06233 |