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

By Michael J. Kearns

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a few vital issues in computational studying concept for researchers and scholars in man made intelligence, neural networks, theoretical computing device technological know-how, and statistics.Computational studying thought is a brand new and swiftly increasing sector of analysis that examines formal versions of induction with the targets of researching the typical equipment underlying effective studying algorithms and opting for the computational impediments to learning.Each subject within the booklet has been selected to clarify a normal precept, that's explored in an actual formal surroundings. instinct has been emphasised within the presentation to make the cloth obtainable to the nontheoretician whereas nonetheless supplying distinctive arguments for the professional. This stability is the results of new proofs of proven theorems, and new shows of the traditional proofs.The themes coated comprise the incentive, definitions, and basic effects, either confident and adverse, for the commonly studied L. G. Valiant version of potentially nearly right studying; Occam's Razor, which formalizes a dating among studying and knowledge compression; the Vapnik-Chervonenkis size; the equivalence of susceptible and robust studying; effective studying within the presence of noise by means of 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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B. We say that L is an efficient (a, {3)-Occam algorithm if its running time is bounded b y a polynomial in n, m and size(c). In what sense is the output let us assume that m > > n, h of an Occam algorithm succinct? First so that the above bound can be effectivel y Copyrighted Material Chapter 2 34 simplified to size( h) < mfJ for some {3 < 1. Since the hypothesis h is consistent with the sample S, h allows us to reconstruct the m labels C(Xl} = h(xd, . , c(xm) = h(xm) given only the unlabeled sequence of instances x}, .

However, the new algo rithm has to carefully choose which literals of h it excludes in order to ensure that the hypothes is grows is still consistent with all the negative examples in S. To do this, we cast the problem as an instance of the Set Cover Problem and apply the greedy algorithm. For each literal z appearing in h, we can identi fy a subset of the negative examples in S. with N6 � S the property that inclusion of z in the hyp othesis conjunc tion is sufficient to guarantee consistency w ith N,.

G. Valiant [92], and was elaborated upon in his two subsequent papers [91, 93). Much of this book is devoted to results in this probabilistic model. Papers by Haussler [45, 46, 47, 44J and Kearns, Li, Pitt and Valiant [59] describe some results in the PAC mod el from an artificial intelligence perspective. 3. The informal rectangle game which began our study was formally analyzed in the PAC model in another im­ portant paper due to Blumer, Ehrenfeucht, Haussler and Warmuth {221, whose main results are the topic of Chapter 3 .

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