Some improved sample complexity bounds in the probabilistic PAC learning model

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 引用 (Scopus)

抜粋

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/e2) 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.

元の言語英語
ホスト出版物のタイトルAlgorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings
編集者Shuji Doshita, Koichi Furukawa, Klaus P. Jantke, Toyaki Nishida
出版者Springer Verlag
ページ208-219
ページ数12
ISBN(印刷物)9783540573692
DOI
出版物ステータス出版済み - 1 1 1993
外部発表Yes
イベント3rd Workshop on Algorithmic Learning Theory, ALT 1992 - Tokyo, 日本
継続期間: 10 20 199210 22 1992

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
743 LNAI
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他3rd Workshop on Algorithmic Learning Theory, ALT 1992
日本
Tokyo
期間10/20/9210/22/92

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • これを引用

    Takeuchi, J. I. (1993). Some improved sample complexity bounds in the probabilistic PAC learning model. : S. Doshita, K. Furukawa, K. P. Jantke, & T. Nishida (版), 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); 巻数 743 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-57369-0_40