Bayesian Support Vector Regression With Automatic Relevance Determination Kernel for Modeling of Antenna Input Characteristics

The modeling of microwave antennas and devices typically requires that non-linear input-output mappings be determined between a set of variable parameters (such as geometry dimensions and frequency), and the corresponding scattering parameter(s). Support vector regression (SVR) employing an isotropic Gaussian kernel has been widely used for such tasks; this kernel has one tunable hyperparameter that can be optimized (along with the penalty constant C) using a standard procedure that involves a parameter grid search combined with cross-validation. The isotropic kernel however suffers from limited expressiveness, and might provide inadequate predictive accuracy for nonlinear mappings that involve multiple tunable input variables. The present study shows that Bayesian support vector regression using the inherently more flexible Gaussian kernel with automatic relevance determination (ARD) is eminently suitable for highly non-linear modeling tasks, such as the input reflection coefficient magnitude |S₁₁| of broadband and ultrawideband antennas. The Bayesian framework enables efficient training of the multiple kernel ARD hyperparameters-a task that would be computationally infeasible for the grid search/cross-validation approach of standard SVR.