Entangled Kernels - Beyond Separability

Riikka Huusari (1, 2) , Hachem Kadri (3)

1 Aalto University School of Science and Technology [Aalto, Finland]
2 HIIT - Helsinki Institute for Information Technology
3 QARMA - éQuipe d'AppRentissage de MArseille

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.

Mots clés: Kernel Learning; Entangled Kernels; Operator-valued Kernels; Vector-valued RKHS; Multi-output Learning

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]

Riikka Huusari, Hachem Kadri. Entangled Kernels - Beyond Separability. Journal of Machine Learning Research, 2021, 22. ⟨hal-03106783⟩