Entangled Kernels -- Beyond Separability

TL;DR

This paper introduces a novel class of entangled operator-valued kernels that go beyond traditional separable kernels, using quantum-inspired tools to improve multi-output regression tasks.

Contribution

It proposes a new framework for operator-valued kernels incorporating entangled kernels and develops an efficient algorithm based on kernel alignment for learning these kernels.

Findings

Entangled kernels outperform separable kernels in multi-output regression.

The proposed algorithm effectively learns complex kernel structures.

Application to real data demonstrates practical advantages.

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.