PAC Learning under Helpful Distributions

François Denis; Rémi Gilleron

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 2, page 129-148
  • ISSN: 0988-3754

Abstract

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A PAC teaching model -under helpful distributions -is proposed which introduces the classical ideas of teaching models within the PAC setting: a polynomial-sized teaching set is associated with each target concept; the criterion of success is PAC identification; an additional parameter, namely the inverse of the minimum probability assigned to any example in the teaching set, is associated with each distribution; the learning algorithm running time takes this new parameter into account. An Occam razor theorem and its converse are proved. Some classical classes of boolean functions, such as Decision Lists, DNF and CNF formulas are proved learnable in this model. Comparisons with other teaching models are made: learnability in the Goldman and Mathias model implies PAC learnability under helpful distributions. Note that Decision lists and DNF are not known to be learnable in the Goldman and Mathias model. A new simple PAC model, where "simple" refers to Kolmogorov complexity, is introduced. We show that most learnability results obtained within previously defined simple PAC models can be simply derived from more general results in our model.

How to cite

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Denis, François, and Gilleron, Rémi. "PAC Learning under Helpful Distributions." RAIRO - Theoretical Informatics and Applications 35.2 (2010): 129-148. <http://eudml.org/doc/222076>.

@article{Denis2010,
abstract = { A PAC teaching model -under helpful distributions -is proposed which introduces the classical ideas of teaching models within the PAC setting: a polynomial-sized teaching set is associated with each target concept; the criterion of success is PAC identification; an additional parameter, namely the inverse of the minimum probability assigned to any example in the teaching set, is associated with each distribution; the learning algorithm running time takes this new parameter into account. An Occam razor theorem and its converse are proved. Some classical classes of boolean functions, such as Decision Lists, DNF and CNF formulas are proved learnable in this model. Comparisons with other teaching models are made: learnability in the Goldman and Mathias model implies PAC learnability under helpful distributions. Note that Decision lists and DNF are not known to be learnable in the Goldman and Mathias model. A new simple PAC model, where "simple" refers to Kolmogorov complexity, is introduced. We show that most learnability results obtained within previously defined simple PAC models can be simply derived from more general results in our model. },
author = {Denis, François, Gilleron, Rémi},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {PAC learning; teaching model; Kolmogorov complexity.; PAC teaching model; learnability},
language = {eng},
month = {3},
number = {2},
pages = {129-148},
publisher = {EDP Sciences},
title = {PAC Learning under Helpful Distributions},
url = {http://eudml.org/doc/222076},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Denis, François
AU - Gilleron, Rémi
TI - PAC Learning under Helpful Distributions
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 129
EP - 148
AB - A PAC teaching model -under helpful distributions -is proposed which introduces the classical ideas of teaching models within the PAC setting: a polynomial-sized teaching set is associated with each target concept; the criterion of success is PAC identification; an additional parameter, namely the inverse of the minimum probability assigned to any example in the teaching set, is associated with each distribution; the learning algorithm running time takes this new parameter into account. An Occam razor theorem and its converse are proved. Some classical classes of boolean functions, such as Decision Lists, DNF and CNF formulas are proved learnable in this model. Comparisons with other teaching models are made: learnability in the Goldman and Mathias model implies PAC learnability under helpful distributions. Note that Decision lists and DNF are not known to be learnable in the Goldman and Mathias model. A new simple PAC model, where "simple" refers to Kolmogorov complexity, is introduced. We show that most learnability results obtained within previously defined simple PAC models can be simply derived from more general results in our model.
LA - eng
KW - PAC learning; teaching model; Kolmogorov complexity.; PAC teaching model; learnability
UR - http://eudml.org/doc/222076
ER -

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