Entangled Kernels - Beyond Separability

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-01
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Mcode
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Language
en
Pages
40
1-40
Series
Journal of Machine Learning Research, Volume 22
Abstract
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and entanglement, we propose a new view on operator-valued kernels and define a general family of kernels that encompasses previously known operator-valued kernels, including separable and transformable kernels. Within this framework, we introduce another novel class of operator-valued kernels called entangled kernels that are not separable. We propose an efficient two-step algorithm for this framework, where the entangled kernel is learned based on a novel extension of kernel alignment to operator-valued kernels. We illustrate our algorithm with an application to supervised dimensionality reduction, and demonstrate its effectiveness with both artificial and real data for multi-output regression.
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Citation
Huusari , R & Kadri , H 2021 , ' Entangled Kernels - Beyond Separability ' , Journal of Machine Learning Research , vol. 22 , pp. 1-40 . < https://jmlr.org/papers/v22/19-665.html >