Communications of the ACM
Computational limitations on learning from examples
Journal of the ACM (JACM)
The Strength of Weak Learnability
Machine Learning
Results on learnability and the Vapnik-Chervonenkis dimension
Information and Computation
Learning Boolean Functions in an Infinite Attribute Space
Machine Learning
C4.5: programs for machine learning
C4.5: programs for machine learning
The nature of statistical learning theory
The nature of statistical learning theory
PAC learning of concept classes through the boundaries of their items
Theoretical Computer Science
Cognitive Systems Research
BICA: A Boolean Indepenedent Component Analysis Approach
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Feature selection via Boolean independent component analysis
Information Sciences: an International Journal
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We present a Probably Approximate Correct (PAC) learning paradigm for boolean formulas, which we call PAC meditation, where the class of formulas to be learnt are not known in advance. On the contrary we split the building of the hypothesis in various levels of increasing description complexity according to additional constraints received at run time. In particular, starting from atomic forms constituted by clauses and monomials learned from the examples at the 0-level, we provide a procedure for computing hypotheses in the various layers of a polynomial hierarchy including k_term-DNF formulas at the second level. Assessment of the sample complexity is based on the notion of sentry functions, introduced in a previous paper, which extends naturally to the various levels of the learning procedure.We make a distinction between meditations whichwaste some sample information and those which exploit all information at each description level, and propose a procedure that is free from information waste. The procedure takes only a polynomial time if we restrict us to learn an inner and outer boundary to the target formula in the polynomial hierarchy, while an access to an NP-oracle is needed if we want to fix the hypothesis in a proper representation.