Fully Empirical and Data-Dependent Stability-Based Bounds

The purpose of this paper is to obtain a fully empir- ical stability-based bound on the generalization ability of a learning procedure, thus, circumventing some limitations of the structural risk minimization framework. We show that assum- ing a desirable property of a learning algorithm is sufficient to make data-dependency explicit for stability, which, instead, is usually bounded only in an algorithmic-dependent way. In addi- tion, we prove that a well-known and widespread classifier, like the support vector machine (SVM), satisfies this condition. The obtained bound is then exploited for model selection purposes in SVM classification and tested on a series of real-world bench- marking datasets demonstrating, in practice, the effectiveness of our approach.