Partial Trace Regression and Low-Rank Kraus Decomposition

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 >

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https://urn.fi/URN:NBN:fi:aalto-202106027172

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[article-cris] Perustieteiden korkeakoulu / SCI

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Partial Trace Regression and Low-Rank Kraus Decomposition

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