### 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: Theoretical Informatics - 7th Latin American Symposium, Proceedings |

Pages | 323-336 |

Number of pages | 14 |

Volume | 3887 LNCS |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*LATIN 2006: Theoretical Informatics - 7th Latin American Symposium, Proceedings*(Vol. 3887 LNCS, 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

**Efficient computation of the relative entropy of probabilistic automata.** / Cortes, Corinna; Mohri, Mehryar; Rastogi, Ashish; Riley, Michael D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*LATIN 2006: Theoretical Informatics - 7th Latin American Symposium, Proceedings.*vol. 3887 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3887 LNCS, pp. 323-336, LATIN 2006: Theoretical Informatics - 7th Latin American Symposium, Valdivia, Chile, 3/20/06. https://doi.org/10.1007/11682462_32

}

TY - GEN

T1 - Efficient computation of the relative entropy of probabilistic automata

AU - Cortes, Corinna

AU - Mohri, Mehryar

AU - Rastogi, Ashish

AU - Riley, Michael D.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745625833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745625833&partnerID=8YFLogxK

U2 - 10.1007/11682462_32

DO - 10.1007/11682462_32

M3 - Conference contribution

AN - SCOPUS:33745625833

SN - 354032755X

SN - 9783540327554

VL - 3887 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 323

EP - 336

BT - LATIN 2006: Theoretical Informatics - 7th Latin American Symposium, Proceedings

ER -