Sufficient Conditions for Uniform Stability of Regularization Algorithms
Name
MIT-CSAIL-TR-2009-060.pdf
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284.79 KB
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Author(s)
Poggio, Tomaso
Rosasco, Lorenzo
Wibisono, Andre
Advisor(s)
Tomaso Poggio
Date Issued
December 1, 2009
Series/Report no.
CBCL-284
MIT-CSAIL-TR-2009-060
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 <= 2 and elastic-net regularization are uniformly ?-stable, and therefore generalize.
Subjects
artificial intelligence
theory
computation
learning
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