### Abstract

Various authors have proposed probabilistic extensions of Valiant's PAC learning model in which the target to be learned is a conditional (or unconditional) probability distribution. In this paper, we improve upon the best known upper bounds on the sample complexity of learning an important class of stochastic rules called ‘stochastic rules with finite partitioning’ with respect to the classic notion of distance between distributions, the Kullback-Leibler divergence (KL-divergence). In particular, we improve the upper bound of order O(1/e^{2}) due to Abe, Takeuchi, and Warmuth [2] to a bound of order O(1/e). Our proof technique is interesting for at least two reasons: First, previously known upper bounds with respect to the KL-divergence were obtained using the uniform convergence technique, while our improved upper bound is obtained by taking advantage of the properties of the maximum likelihood estimator. Second, our proof relies on the fact that only a linear number of examples are required in order to distinguish a true parametric model from a bad parametric model. The latter notion is apparently related to the notion of discrimination proposed and studied by Yamanishi, but the exact relationship is yet to be determined.

Original language | English |
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Title of host publication | Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings |

Editors | Shuji Doshita, Koichi Furukawa, Klaus P. Jantke, Toyaki Nishida |

Publisher | Springer Verlag |

Pages | 208-219 |

Number of pages | 12 |

ISBN (Print) | 9783540573692 |

DOIs | |

Publication status | Published - Jan 1 1993 |

Event | 3rd Workshop on Algorithmic Learning Theory, ALT 1992 - Tokyo, Japan Duration: Oct 20 1992 → Oct 22 1992 |

### 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 | 743 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithmic Learning Theory, ALT 1992 |
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Country | Japan |

City | Tokyo |

Period | 10/20/92 → 10/22/92 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings*(pp. 208-219). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 743 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57369-0_40