Refutably probably approximately correct learning

Satoshi Matsumoto, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We propose a notion of the refutably PAC learning, which formalizes the refutability of hypothesis spaces in the PAC learning model. Intuitively, the refutably PAC learning for a concept class F requires that the learning algorithm should refute F with high probability if a target concept can not be approximated by any concept in F with respect to the underlying probability distribution. We give a general upper bound of O((1/ε + 1 + 1/ ε′) ln (|F[n]|/δ)) on the number of examples required for refutably PAC learning of F. Here, ε and δ are the standard accuracy and confidence parameters, and ε′ is the refutation accuracy. Furthermore we also define the strongly refutably PAC learning by introducing the refutation threshold. We prove a general upper bound of O((1/ε2 + 1/ε′2) In (|F[n]|/δ)) for strongly refutably PAC learning of F. These upper bounds reveal that both the refutably learnability and the strongly refutably learnability are equivalent to the standard learnability within the polynomial size restriction. We also define the polynomialtime refutably learnability of a concept class, and characterize it.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 4th International Workshop on Analogical and Inductive Inference, AII 1994 and 5th International Workshop on Algorithmic Learning Theory, ALT 1994, Proceedings
EditorsSetsuo Arikawa, Klaus P. Jantke
PublisherSpringer Verlag
Pages469-483
Number of pages15
ISBN (Print)9783540585206
DOIs
Publication statusPublished - 1994
Externally publishedYes
Event4th International Workshop on Analogical and Inductive Inference, AII 1994 and 5th International Workshop on Algorithmic Learning Theory, ALT 1994 - Reinhardsbrunn Castle, Germany
Duration: 1994 Oct 101994 Oct 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume872 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Workshop on Analogical and Inductive Inference, AII 1994 and 5th International Workshop on Algorithmic Learning Theory, ALT 1994
CountryGermany
CityReinhardsbrunn Castle
Period94/10/1094/10/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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