Comment on "robustness and regularization of support vector machines" by H. Xu, et al., (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2009, arXiv:0803.3490)

TL;DR

This paper critically examines a theorem on the relationship between robustness in feature and sample spaces for support vector machines, providing a counterexample that challenges the original claim.

Contribution

It presents a counterexample that refutes Xu et al.'s theorem linking robustness in feature and sample spaces for SVMs.

Findings

Counterexample invalidates the theorem

Challenges assumptions about robustness equivalence

Questions previous theoretical claims

Abstract

This paper comments on the published work dealing with robustness and regularization of support vector machines (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2009) [arXiv:0803.3490] by H. Xu, etc. They proposed a theorem to show that it is possible to relate robustness in the feature space and robustness in the sample space directly. In this paper, we propose a counter example that rejects their theorem.