Entangled Kernels -- Beyond Separability

• URL: http://arxiv.org/abs/2101.05514v1
• Date: Thu, 14 Jan 2021 09:18:02 GMT
• Title: Entangled Kernels -- Beyond Separability
• Authors: Riikka Huusari, Hachem Kadri
• Abstract summary: We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. We propose a new view on operator-valued kernels and define a general family of kernels that encompasses previously known operator-valued kernels. Within this framework, we introduce another novel class of operator-valued kernels called entangled kernels that are not separable.
• Score: 10.381276986079865
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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