Abstract
We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the standard deviation of the noise and in particular approach zero in the exact recovery case; (2) even in the presence of noise, they converge to zero when the sample size approaches infinity; and (3) for a fixed dimension of the side information, they only have a logarithmic dependence on the size of the matrix. Differently from many works in approximate recovery, we present results both for bounded Lipschitz losses and for the absolute loss, with the latter relying on Talagrand-type inequalities. The proofs create a bridge between two approaches to the theoretical analysis of matrix completion, since they consist in a combination of techniques from both the exact recovery literature and the approximate recovery literature.
Original language | English |
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Title of host publication | Proceedings of the 37th AAAI Conference on Artificial Intelligence |
Editors | Brian Williams, Yiling Chen, Jennifer Neville |
Place of Publication | Washington, DC |
Publisher | AAAI press |
Pages | 8447-8455 |
Number of pages | 9 |
ISBN (Electronic) | 9781577358800 |
DOIs | |
Publication status | Published - 27 Jun 2023 |
Event | 37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States Duration: 7 Feb 2023 → 14 Feb 2023 https://ojs.aaai.org/index.php/AAAI/issue/view/553 https://aaai-23.aaai.org/ |
Publication series
Name | Proceedings of the AAAI Conference on Artificial Intelligence |
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Publisher | AAAI Press |
Number | 7 |
Volume | 37 |
ISSN (Print) | 2159-5399 |
ISSN (Electronic) | 2374-3468 |
Conference
Conference | 37th AAAI Conference on Artificial Intelligence, AAAI 2023 |
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Country/Territory | United States |
City | Washington |
Period | 7/02/23 → 14/02/23 |
Internet address |
Scopus Subject Areas
- Artificial Intelligence