Predictive Low Rank Matrix Learning Under Partial Observations: Mixed-Projection ADMM.
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| Title: | Predictive Low Rank Matrix Learning Under Partial Observations: Mixed-Projection ADMM. |
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| Authors: | Bertsimas, Dimitris1 (AUTHOR) dbertsim@mit.edu, Johnson, Nicholas A. G.2 (AUTHOR) nagj@mit.edu |
| Source: | Machine Learning. Jun2026, Vol. 115 Issue 6, p1-53. 53p. |
| Abstract: | We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that arises in applications such as recommendation systems, signal processing, system identification and image denoising. We formalize this problem as an optimization problem with an objective that balances the strength of the fit of the reconstruction to the observed entries with the ability of the reconstruction to be predictive of the side information. We derive a mixed-projection reformulation of the resulting optimization problem and present a strong semidefinite cone relaxation. We design an efficient, scalable alternating direction method of multipliers algorithm that produces high quality feasible solutions to the problem of interest. Our numerical results demonstrate that in the small rank regime (), our algorithm outputs solutions that achieve on average lower objective value and lower reconstruction error than the solutions returned by the best performing benchmark method on synthetic data. The runtime of our algorithm is competitive with and often superior to that of the benchmark methods. Our algorithm is able to solve problems with rows and columns in less than a minute. On large scale real world data, our algorithm produces solutions that achieve lower out of sample error than benchmark methods in less execution time. [ABSTRACT FROM AUTHOR] |
| Copyright of Machine Learning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 193999614 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Predictive Low Rank Matrix Learning Under Partial Observations: Mixed-Projection ADMM. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bertsimas%2C+Dimitris%22">Bertsimas, Dimitris</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dbertsim@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Johnson%2C+Nicholas+A%2E+G%2E%22">Johnson, Nicholas A. G.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> nagj@mit.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Machine+Learning%22">Machine Learning</searchLink>. Jun2026, Vol. 115 Issue 6, p1-53. 53p. – Name: Abstract Label: Abstract Group: Ab Data: We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that arises in applications such as recommendation systems, signal processing, system identification and image denoising. We formalize this problem as an optimization problem with an objective that balances the strength of the fit of the reconstruction to the observed entries with the ability of the reconstruction to be predictive of the side information. We derive a mixed-projection reformulation of the resulting optimization problem and present a strong semidefinite cone relaxation. We design an efficient, scalable alternating direction method of multipliers algorithm that produces high quality feasible solutions to the problem of interest. Our numerical results demonstrate that in the small rank regime (), our algorithm outputs solutions that achieve on average lower objective value and lower reconstruction error than the solutions returned by the best performing benchmark method on synthetic data. The runtime of our algorithm is competitive with and often superior to that of the benchmark methods. Our algorithm is able to solve problems with rows and columns in less than a minute. On large scale real world data, our algorithm produces solutions that achieve lower out of sample error than benchmark methods in less execution time. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Machine Learning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10994-026-07005-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 53 StartPage: 1 Titles: – TitleFull: Predictive Low Rank Matrix Learning Under Partial Observations: Mixed-Projection ADMM. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bertsimas, Dimitris – PersonEntity: Name: NameFull: Johnson, Nicholas A. G. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 08856125 Numbering: – Type: volume Value: 115 – Type: issue Value: 6 Titles: – TitleFull: Machine Learning Type: main |
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