Computationally Stable QCQP and SDP Multikernel Support Vector Regression Formulations

Abstract

This study will explore alternative versions of the Multikernel Support Vector Regressor (SVR) algorithm. The two versions that will be explored include a derivation that uses an Objective-to-Constraint transformation to derive a Quadratically Constrained Quadratic Program (QCQP) algorithm with computational advantages over the earlier formulations. For the other approach, an innovative method to filter support vectors is used to increase numerical stability. This approach uses Lagrangian Duality and Semidefinite Programming (SDP) theory to derive a more general formulation. It will be shown that the alternative QCQP and SDP formulations provide computational advantages over their respective prior formulations, offering a more practical alternative to manual kernel design, especially in scenarios where using a multikernel is essential for problem construction, making it an ideal tool for researchers and practitioners.