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Partial Trace Regression and Low-Rank Kraus Decomposition
Hachem Kadri · Stephane Ayache · Riikka Huusari · alain rakotomamonjy · Ralaivola Liva

Tue Jul 14 12:00 PM -- 12:45 PM & Wed Jul 15 01:00 AM -- 01:45 AM (PDT) @ Virtual #None

The trace regression model, a direct extension of the well-studied linear regression model, allows 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.

Author Information

Hachem Kadri (Aix-Marseille University)
Stephane Ayache (AMU LIS)
Riikka Huusari (Aalto University)
alain rakotomamonjy (Universite de Rouen Normandie / Criteo AI Lab)
Ralaivola Liva (Criteo AI Lab)

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