Abstract
The trace regression model, a direct extension of the well-studied linear regression model, al-lows one to map matrices to real-valued outputs.We here introduce an even more general model,namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps.We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.
Original language | English |
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Title of host publication | 37th International Conference on Machine Learning, ICML 2020 |
Pages | 4998-5008 |
Number of pages | 11 |
ISBN (Electronic) | 9781713821120 |
Publication status | Published - 2020 |
MoE publication type | A4 Article in a conference publication |
Event | International Conference on Machine Learning - Vienna, Austria Duration: 12 Jul 2020 → 18 Jul 2020 Conference number: 37 |
Publication series
Name | Proceedings of Machine Learning Research |
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Publisher | MLRP |
Volume | 119 |
ISSN (Electronic) | 2640-3498 |
Conference
Conference | International Conference on Machine Learning |
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Abbreviated title | ICML |
Country/Territory | Austria |
City | Vienna |
Period | 12/07/2020 → 18/07/2020 |