Sufficient Conditions for Uniform Stability of Regularization Algorithms

Wibisono A., Rosasco L., Poggio T.,

CSAIL Technical Report , MIT-CSAIL-TR-2009-060/CBCL284 , Massachusetts Institute of Technology, Cambridge, MA , December 1, 2009

Citable URI: http://hdl.handle.net/1721.1/49868

Abstract: 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 [3], 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

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