### Abstract

In order to understand AdaBoost's dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases. We find stable cycles for these cases, which can explicitly be used to solve for Ada- Boost's output. By considering AdaBoost as a dynamical system, we are able to prove R̈atsch and Warmuth's conjecture that AdaBoost may fail to converge to a maximal-margin combined classifier when given a 'nonoptimal' weak learning algorithm. AdaBoost is known to be a coordinate descent method, but other known algorithms that explicitly aim to maximize the margin (such as AdaBoost and arc-gv) are not. We consider a differentiable function for which coordinate ascent will yield a maximum margin solution. We then make a simple approximation to derive a new boosting algorithm whose updates are slightly more aggressive than those of arcgv.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003 |

Publisher | Neural information processing systems foundation |

ISBN (Print) | 0262201526, 9780262201520 |

State | Published - Jan 1 2004 |

Event | 17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada Duration: Dec 8 2003 → Dec 13 2003 |

### Publication series

Name | Advances in Neural Information Processing Systems |
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ISSN (Print) | 1049-5258 |

### Other

Other | 17th Annual Conference on Neural Information Processing Systems, NIPS 2003 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/8/03 → 12/13/03 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing

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## Cite this

*Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003*(Advances in Neural Information Processing Systems). Neural information processing systems foundation.