Sufficient Conditions for Uniform Stability of Regularization Algorithms
Author(s)Poggio, Tomaso; Rosasco, Lorenzo; Wibisono, Andre
Center for Biological and Computational Learning (CBCL)
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In this paper, we study the stability and generalization properties of penalized empirical-risk minimization algorithms. We propose a set of properties of the penalty term that is sufficient to ensure uniform ?-stability: we show that if the penalty function satisfies a suitable convexity property, then the induced regularization algorithm is uniformly ?-stable. In particular, our results imply that regularization algorithms with penalty functions which are strongly convex on bounded domains are ?-stable. In view of the results in , uniform stability implies generalization, and moreover, consistency results can be easily obtained. We apply our results to show that â p regularization for 1 < p <= 2 and elastic-net regularization are uniformly ?-stable, and therefore generalize.
artificial intelligence, theory, computation, learning