Robustness of learning algorithms using hinge loss with outlier indicators. (October 2017)

• Record Type: Journal Article
• Authors: Kanamori, Takafumi; Fujiwara, Shuhei; Takeda, Akiko
• Is Part Of: Neural networks. Volume 94(2017)
• Page Start: 173
• Page End: 191
• Publication Date: 2017-10
• Subjects: Breakdown point -- Support vector machines -- Non-convex optimization -- Local optima; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2017.07.005
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: We propose a unified formulation of robust learning methods for classification and regression problems. In the learning methods, the hinge loss is used with outlier indicators in order to detect outliers in the observed data. To analyze the robustness property, we evaluate the breakdown point of the learning methods in the situation that the outlier ratio is not necessarily small. Although minimization of the hinge loss with outlier indicators is a non-convex optimization problem, we prove that any local optimal solution of our learning algorithms has the robustness property. The theoretical findings are confirmed in numerical experiments.