Partial Trace Regression and Low-Rank Kraus Decomposition

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Conference article in proceedings
Date
2020
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Mcode
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Language
en
Pages
11
4998-5008
Series
37th International Conference on Machine Learning, ICML 2020, Proceedings of Machine Learning Research, Volume 119
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.
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Kadri , H , Ayache , S , Huusari , R , Rakotomamonjy , A & Ralaivola , L 2020 , Partial Trace Regression and Low-Rank Kraus Decomposition . in 37th International Conference on Machine Learning, ICML 2020 . Proceedings of Machine Learning Research , vol. 119 , International Machine Learning Society , pp. 4998-5008 , International Conference on Machine Learning , Vienna , Austria , 12/07/2020 . < http://proceedings.mlr.press/v119/kadri20a.html >