Knowledge-Based Kernel Approximation

Abstract

Prior knowledge, in the form of linear inequalities that need to be satisfied over multiple polyhedral sets, is incorporated into a function approximation generated by a linear combination of linear or nonlinear kernels. In addition, the approximation needs to satisfy conventional conditions such as having given exact or inexact function values at certain points. Determining such an approximation leads to a linear programming formulation. By using nonlinear kernels and mapping the prior polyhedral knowledge in the input space to one defined by the kernels, the prior knowledge translates into nonlinear inequalities in the original input space. Through a number of computational examples, including a real world breast cancer prognosis dataset, it is shown that prior knowledge can significantly improve function approximation.