Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms
We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive...
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| Format: | Conference item |
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Neural information processing systems foundation
2013
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| _version_ | 1826267446485450752 |
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| author | Todeschini, A Caron, F Chavent, M |
| author_facet | Todeschini, A Caron, F Chavent, M |
| author_sort | Todeschini, A |
| collection | OXFORD |
| description | We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an Expectation-Maximization algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low rank matrix completion. |
| first_indexed | 2024-03-06T20:54:20Z |
| format | Conference item |
| id | oxford-uuid:38a98cc2-e501-46b0-b013-bad5e7eb8c02 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:54:20Z |
| publishDate | 2013 |
| publisher | Neural information processing systems foundation |
| record_format | dspace |
| spelling | oxford-uuid:38a98cc2-e501-46b0-b013-bad5e7eb8c022022-03-26T13:51:25ZProbabilistic low-rank matrix completion with adaptive spectral regularization algorithmsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:38a98cc2-e501-46b0-b013-bad5e7eb8c02Symplectic Elements at OxfordNeural information processing systems foundation2013Todeschini, ACaron, FChavent, MWe propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an Expectation-Maximization algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low rank matrix completion. |
| spellingShingle | Todeschini, A Caron, F Chavent, M Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title | Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title_full | Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title_fullStr | Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title_full_unstemmed | Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title_short | Probabilistic low-rank matrix completion with adaptive spectral regularization algorithms |
| title_sort | probabilistic low rank matrix completion with adaptive spectral regularization algorithms |
| work_keys_str_mv | AT todeschinia probabilisticlowrankmatrixcompletionwithadaptivespectralregularizationalgorithms AT caronf probabilisticlowrankmatrixcompletionwithadaptivespectralregularizationalgorithms AT chaventm probabilisticlowrankmatrixcompletionwithadaptivespectralregularizationalgorithms |