Boosting Algorithms for Maximizing the Soft Margin

Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)

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Gunnar Rätsch, Manfred K. K. Warmuth, Karen Glocer


Gunnar R¨atsch

Friedrich Miescher Laboratory

Max Planck Society T¨ubingen, Germany

We present a novel boosting algorithm, called SoftBoost, designed for sets of bi- nary labeled examples that are not necessarily separable by convex combinations of base hypotheses. Our algorithm achieves robustness by capping the distribu- tions on the examples. Our update of the distribution is motivated by minimizing a relative entropy subject to the capping constraints and constraints on the edges of the obtained base hypotheses. The capping constraints imply a soft margin in the dual optimization problem. Our algorithm produces a convex combination of hypotheses whose soft margin is within δ of its maximum. We employ relative en- tropy projection methods to prove an O( ln N δ2 ) iteration bound for our algorithm, where N is number of examples. We compare our algorithm with other approaches including LPBoost, Brown- Boost, and SmoothBoost. We show that there exist cases where the number of iter- ations required by LPBoost grows linearly in N instead of the logarithmic growth for SoftBoost. In simulation studies we show that our algorithm converges about as fast as LPBoost, faster than BrownBoost, and much faster than SmoothBoost. In a benchmark comparison we illustrate the competitiveness of our approach.