< Back to previous page

Publication

On consistency and robustness properties of Support Vector Machines for heavy-tailed distributions

Journal Contribution - Journal Article

Support Vector Machines (SVMs) are known to be consistent and robust for classification and regression if they are based on a Lipschitz continuous loss function and on a bounded kernel with a dense and separable reproducing kernel Hilbert space. These facts are even true in the regression context for unbounded output spaces, if the target function f is integrable with respect to the marginal distribution of
the input variable X and if the output variable Y has a finite first absolute moment. The latter assumption clearly excludes distributions with heavy tails, e.g., several stable distributions or some extreme value distributions which occur in financial or insurance projects. The main point of this paper is that we can enlarge the applicability of SVMs even to heavy-tailed distributions, which violate this moment condition. Results on existence, uniqueness, representation, consistency, and statistical robustness are given.
Journal: Statistics
ISSN: 1938-7989
Volume: 2
Pages: 311-327
Publication year:2009
Keywords:Robustness, Consistency, Support Vector Machine, Regularized empirical risk minimization, Bouligand influence function, Heavy tails