### Abstract

The problem of the efficient computation of the relative entropy of two distributions represented by deterministic weighted automata arises in several machine learning problems. We show that this problem can be naturally formulated as a shortest-distance problem over an intersection automaton denned on an appropriate semiring. We describe simple and efficient novel algorithms for its computation and report the results of experiments demonstrating the practicality of our algorithms for very large weighted automata. Our algorithms apply to unambiguous weighted automata, a class of weighted automata that strictly includes deterministic weighted automata. These are also the first algorithms extending the computation of entropy or of relative entropy beyond the class of deterministic weighted automata.

Original language | English (US) |
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Title of host publication | LATIN 2006 |

Subtitle of host publication | Theoretical Informatics - 7th Latin American Symposium, Proceedings |

Pages | 323-336 |

Number of pages | 14 |

DOIs | |

State | Published - 2006 |

Event | LATIN 2006: Theoretical Informatics - 7th Latin American Symposium - Valdivia, Chile Duration: Mar 20 2006 → Mar 24 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3887 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | LATIN 2006: Theoretical Informatics - 7th Latin American Symposium |
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Country | Chile |

City | Valdivia |

Period | 3/20/06 → 3/24/06 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*LATIN 2006: Theoretical Informatics - 7th Latin American Symposium, Proceedings*(pp. 323-336). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3887 LNCS). https://doi.org/10.1007/11682462_32