2010 | OriginalPaper | Chapter
Approximation Stability and Boosting
Authors : Wei Gao, Zhi-Hua Zhou
Published in: Algorithmic Learning Theory
Publisher: Springer Berlin Heidelberg
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Stability has been explored to study the performance of learning algorithms in recent years and it has been shown that stability is sufficient for generalization and is sufficient and necessary for consistency of ERM in the general learning setting. Previous studies showed that AdaBoost has almost-everywhere uniform stability if the base learner has
L
1
stability. The
L
1
stability, however, is too restrictive and we show that AdaBoost becomes constant learner if the base learner is not real-valued learner. Considering that AdaBoost is mostly successful as a classification algorithm, stability analysis for AdaBoost when the base learner is not real-valued learner is an important yet unsolved problem. In this paper, we introduce the
approximation stability
and prove that approximation stability is sufficient for generalization, and sufficient and necessary for learnability of AERM in the general learning setting. We prove that AdaBoost has approximation stability and thus has good generalization, and an exponential bound for AdaBoost is provided.