Generalization Analysis of Fredholm Kernel Regularized Classifiers

Recently, a new framework, Fredholm learning, was proposed for semisupervised learning problems based on solving a regularized Fredholm integral equation. It allows a natural way to incorporate unlabeled data into learning algorithms to improve their prediction performance. Despite rapid progress on implementable algorithms with theoretical guarantees, the generalization ability of Fredholm kernel learning has not been studied. In this letter, we focus on investigating the generalization performance of a family of classification algorithms, referred to as Fredholm kernel regularized classifiers. We prove that the corresponding learning rate can achieve ( is the number of labeled samples) in a limiting case. In addition, a representer theorem is provided for the proposed regularized scheme, which underlies its applications.