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An Introduction to Computational Learning Theory - download pdf or read online

By Michael J. Kearns

ISBN-10: 0262111934

ISBN-13: 9780262111935

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a few important issues in computational studying thought for researchers and scholars in man made intelligence, neural networks, theoretical laptop technology, and statistics.Computational studying thought is a brand new and speedily increasing region of study that examines formal types of induction with the objectives of getting to know the typical equipment underlying effective studying algorithms and making a choice on the computational impediments to learning.Each subject within the booklet has been selected to clarify a common precept, that is explored in an actual formal environment. instinct has been emphasised within the presentation to make the fabric obtainable to the nontheoretician whereas nonetheless offering distinct arguments for the expert. This stability is the results of new proofs of demonstrated theorems, and new shows of the normal proofs.The themes coated comprise the inducement, definitions, and primary effects, either optimistic and destructive, for the commonly studied L. G. Valiant version of doubtless nearly right studying; Occam's Razor, which formalizes a dating among studying and knowledge compression; the Vapnik-Chervonenkis measurement; the equivalence of vulnerable and robust studying; effective studying within the presence of noise via the tactic of statistical queries; relationships among studying and cryptography, and the ensuing computational boundaries on effective studying; reducibility among studying difficulties; and algorithms for studying finite automata from energetic experimentation.

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Extra resources for An Introduction to Computational Learning Theory

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Evalua­ tion starts at the leftmost item and continues to the right until the first condition is satisfi ed, at which point the binary value below becomes the final result of the evaluation. Figure observe that if a concept c can be represented as a k-decision list, then so can ""Ie (simply complement the values of the bi ) . Clearly, any k­ DNF formula can be represented as a k-decision list of the same length (choose an arbitrary order in which to evaluate the terms ofthe k-DNF, setting all the bi to 1 and the default b to 0).

3 If RP '# NP, the representation class of 9-term Copyrighted Material DNF Probably Approximately Correct Learning 19 formulae is not efficiently PA C learnable. Proof: The high-level idea of the proof is to reduce an NP-complete la nguage A ( to be specified shortly ) to the problem of PAC learning 3- term DNF formulae. More precisely, the reduction will efficiently map any string �, for which we wish to determine membership in A, to a set So of labeled examples. The cardinality ISol will be bounded by a polynomial in the string length I�I.

We first note that the results of the previous chapt er can be used to give such a bound in the case that C is a concept class of finite cardinality. 2 guarantees that h will meet the PAC model criteria. Notice that this b oun d is not meaningful if C has infinite cardinality. Are there any non- trivial infinite concept classes that are learnable from a finite sample? 1 is an example of such a class. In the analysis of that PAC learning algo rithm , we made critical use of the fact that axis-aligned rectangles have simple boundaries: the target rectangle is always completely specified by four real numbers that indicate the locations of the four bounding edges, and this allowed us to partition the error of the tightest-fit hypothesis into four simple rectilinear regions.

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