Representer Theorem

Abstract

The representer theorem plays an outsized role in a large class of learning problems. It provides a means to reduce infinite dimensional optimization problems to tractable finite dimensional ones. This article reviews the representer theorem for various learning problems under the reproducing kernel Hilbert spaces framework. We present solutions to the penalized least squares and penalized likelihood for nonparametric regression and support vector machines for classification as a solution to the penalized hinge loss. We discuss extensions of the representer theorem for regression with functional data.

Simplex-Based Proximal Multicategory Support Vector Machine

“…For more discussions on the representer theorem, we refer readers to [70], [71], [72], [73], [74], and [75].…”