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The Consistency of Greedy Algorithms for Classification

  • Shie Mannor
  • Ron Meir
  • Tong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2375)

Abstract

We consider a class of algorithms for classification, which are based on sequential greedy minimization of a convex upper bound on the 0 — 1 loss function. A large class of recently popular algorithms falls within the scope of this approach, including many variants of Boosting algorithms. The basic question addressed in this paper relates to the statistical consistency of such approaches. We provide precise conditions which guarantee that sequential greedy procedures are consistent, and establish rates of convergence under the assumption that the Bayes decision boundary belongs to a certain class of smooth functions. The results are established using a form of regularization which constrains the search space at each iteration of the algorithm. In addition to providing general consistency results, we provide rates of convergence for smooth decision boundaries. A particularly interesting conclusion of our work is that Logistic function based Boosting provides faster rates of convergence than Boosting based on the exponential function used in AdaBoost.

Keywords

Loss Function Greedy Algorithm Borel Measurable Function Yorktown Height Computational Learn Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Shie Mannor
    • 1
  • Ron Meir
    • 1
  • Tong Zhang
    • 2
  1. 1.Department of Electrical EngineeringTechnionHaifaIsrael
  2. 2.IBM T. J. Watson Research CenterYorktown HeightsUSA

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