## Abstract

The information bottleneck (IB) method is an information-theoretic formulation for clustering problems. Given a joint distribution (x, y), this method constructs a new variable that defines partitions over the values of X that are informative about Y. Maximum likelihood (ML) of mixture models is a standard statistical approach to clustering problems. In this paper, we ask: how are the two methods related ? We define a simple mapping between the IB problem and the ML problem for the multinomial mixture model. We show that under this mapping the problems are strongly related. In fact, for uniform input distribution over X or for large sample size, the problems are mathematically equivalent. Specifically, in these cases, every fixed point of the IB-functional defines a fixed point of the (log) likelihood and vice versa. Moreover, the values of the functionals at the fixed points are equal under simple transformations. As a result, in these cases, every algorithm that solves one of the problems, induces a solution for the other.

Original language | American English |
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Title of host publication | NIPS 2002 |

Subtitle of host publication | Proceedings of the 15th International Conference on Neural Information Processing Systems |

Editors | Suzanna Becker, Sebastian Thrun, Klaus Obermayer |

Publisher | MIT Press Journals |

Pages | 335-342 |

Number of pages | 8 |

ISBN (Electronic) | 0262025507, 9780262025508 |

State | Published - 2002 |

Event | 15th International Conference on Neural Information Processing Systems, NIPS 2002 - Vancouver, Canada Duration: 9 Dec 2002 → 14 Dec 2002 |

### Publication series

Name | NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems |
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### Conference

Conference | 15th International Conference on Neural Information Processing Systems, NIPS 2002 |
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Country/Territory | Canada |

City | Vancouver |

Period | 9/12/02 → 14/12/02 |

### Bibliographical note

Publisher Copyright:© NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. All rights reserved.