## Abstract

We investigate further improvement of boosting in the case that the target concept belongs to the class of r-of-k threshold Boolean functions, which answer "+1" if at least r of k relevant variables are positive, and answer "-1" otherwise. Given m examples of a r-of-k function and literals as base hypotheses, popular boosting algorithms (e.g., AdaBoost) construct a consistent final hypothesis by using O(k ^{2} log m) base hypotheses. While this convergence speed is tight in general, we show that a modification of AdaBoost (confidence-rated AdaBoost [SS99] or InfoBoost [As100]) can make use of the property of r-of-k functions that make less error on one-side to find a consistent final hypothesis by using O(kr log m) hypotheses. Our result extends the previous investigation by Hatano and Warmuth [HW04] and gives more general examples where confidence-rated AdaBoost or InfoBoost has an advantage over AdaBoost.

Original language | English |
---|---|

Pages (from-to) | 114-126 |

Number of pages | 13 |

Journal | Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) |

Volume | 3244 |

Publication status | Published - Dec 1 2004 |

Externally published | Yes |

Event | 15th International Conference ALT 2004: Algorithmic Learning Theory - Padova, Italy Duration: Oct 2 2004 → Oct 5 2004 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)