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Dominating distributions and learnability

Authors:

Gyora M. Benedek,

Alon ItaiAuthors Info & Claims

COLT '92: Proceedings of the fifth annual workshop on Computational learning theory

Pages 253 - 264

https://doi.org/10.1145/130385.130413

Published: 01 July 1992 Publication History

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Abstract

We consider PAC-learning where the distribution is known to the student. The problem addressed here is characterizing when learnability with respect to distribution D₁ implies learnability with respect to distribution D₂.

The answer to the above question depends on the learnability model. If the number of examples need not be bounded by a polynomial, it is sufficient to require that all sets which have zero probability with respect to D₂ have zero probability with respect to d₁. If the number of examples is required to be polynomial, then the probability with respect to D₂ must be bounded by a multiplicative constant from that of D₁. More stringent conditions must hold if we insist that every hypothesis consistent with the examples be close to the target.

Finally, we address the learnability properties of classes of distributions.

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Cited By

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Najarian K(2005)A Fixed-Distribution PAC Learning Theory for Neural FIR ModelsJournal of Intelligent Information Systems10.1007/s10844-005-0194-y25:3(275-291)Online publication date: 1-Nov-2005
https://dl.acm.org/doi/10.1007/s10844-005-0194-y
Najarian K(2002)FIR Volterra kernel neural models and PAC learningComplexity10.1002/cplx.100427:6(48-55)Online publication date: 19-Dec-2002
https://doi.org/10.1002/cplx.10042
Apollini BGentile C(1999)P-sufficient statistics for PAC learning k-term-DNF formulas through enumerationTheoretical Computer Science10.1016/S0304-3975(98)00215-1230:1-2(1-37)Online publication date: 6-Dec-1999
https://dl.acm.org/doi/10.1016/S0304-3975%2898%2900215-1
Show More Cited By

Index Terms

Dominating distributions and learnability
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Models of computation
    1. Abstract machines

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COLT '92: Proceedings of the fifth annual workshop on Computational learning theory

July 1992

452 pages

ISBN:089791497X

DOI:10.1145/130385

Chairman:
David Haussler

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 1992

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COLT92: 5th Annual Workshop on Computational Learning Theory

July 27 - 29, 1992

Pennsylvania, Pittsburgh, USA

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Najarian K(2005)A Fixed-Distribution PAC Learning Theory for Neural FIR ModelsJournal of Intelligent Information Systems10.1007/s10844-005-0194-y25:3(275-291)Online publication date: 1-Nov-2005
https://dl.acm.org/doi/10.1007/s10844-005-0194-y
Najarian K(2002)FIR Volterra kernel neural models and PAC learningComplexity10.1002/cplx.100427:6(48-55)Online publication date: 19-Dec-2002
https://doi.org/10.1002/cplx.10042
Apollini BGentile C(1999)P-sufficient statistics for PAC learning k-term-DNF formulas through enumerationTheoretical Computer Science10.1016/S0304-3975(98)00215-1230:1-2(1-37)Online publication date: 6-Dec-1999
https://dl.acm.org/doi/10.1016/S0304-3975%2898%2900215-1
Decatur S(1993)Statistical queries and faulty PAC oraclesProceedings of the sixth annual conference on Computational learning theory10.1145/168304.168346(262-268)Online publication date: 1-Aug-1993
https://dl.acm.org/doi/10.1145/168304.168346

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Predictive PAC Learnability: A Paradigm for Learning from Exchangeable Input Data

A Representation for Ellipsoidal Distributions

Dominating Subsets under Projections

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Predictive PAC Learnability: A Paradigm for Learning from Exchangeable Input Data

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Dominating Subsets under Projections

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