Classification with support vector machines and Kolmogorov-Smirnov bounds

Utkin, L.V.; Coolen, F.P.A.

Abstract

This article presents a new statistical inference method for classification. Instead of minimizing a loss function that solely takes residuals into account, it uses the Kolmogorov–Smirnov bounds for the cumulative distribution function of the residuals, as such taking conservative bounds for the underlying probability distribution for the population of residuals into account. The loss functions considered are based on the theory of support vector machines. Parameters for the discriminant functions are computed using a minimax criterion, and for a wide range of popular loss functions, the computations are shown to be feasible based on new optimization results presented in this article. The method is illustrated in examples, both with small simulated data sets and with real-world data.

Citation

Utkin, L., & Coolen, F. (2014). Classification with support vector machines and Kolmogorov-Smirnov bounds. Journal of statistical theory and practice, 8(2), 297-318. https://doi.org/10.1080/15598608.2013.788985

• Journal Article Type: Article
• Publication Date: Mar 24, 2014
• Deposit Date: Apr 11, 2014
• Publicly Available Date: Nov 28, 2014
• Journal: Journal of Statistical Theory and Practice
• Electronic ISSN: 1559-8616
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 2
• Pages: 297-318
• DOI: https://doi.org/10.1080/15598608.2013.788985
• Keywords: Classification, Imprecise probability, Kolmogorov–Smirnov bounds, Minimax, Support vector machines.
• Public URL: https://durham-repository.worktribe.com/output/1435634