Download An Introduction to Computational Learning Theory by Michael J. Kearns PDF

By Michael J. Kearns

ISBN-10: 0262111934

ISBN-13: 9780262111935

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a couple of important themes in computational studying idea for researchers and scholars in man made intelligence, neural networks, theoretical laptop technological know-how, and statistics.Computational studying concept is a brand new and speedily increasing quarter of analysis that examines formal types of induction with the pursuits of gaining knowledge of the typical tools underlying effective studying algorithms and settling on the computational impediments to learning.Each subject within the e-book has been selected to explain a normal precept, that's explored in an actual formal environment. instinct has been emphasised within the presentation to make the cloth available to the nontheoretician whereas nonetheless supplying specified arguments for the professional. This stability is the results of new proofs of tested theorems, and new displays of the traditional proofs.The subject matters lined comprise the incentive, definitions, and primary effects, either optimistic and unfavorable, for the commonly studied L. G. Valiant version of potentially nearly right studying; Occam's Razor, which formalizes a courting among studying and knowledge compression; the Vapnik-Chervonenkis size; the equivalence of susceptible and powerful 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 obstacles on effective studying; reducibility among studying difficulties; and algorithms for studying finite automata from energetic experimentation.

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For this concept class, we can shatter the four points shown in Figure 3 . 3 { a ), where we have again indicated how a single dichotomy can be realized and left the remainder to the reader. 3(b). 2: (a) A dicho tom y and its realization by a hal/space, with the shaded region indicating the positive side. (b) and (c) Dichotomies unre­ alizable by hal/spaces. (a) (b) + + • + • -. -. (c) . + • -+ • • +. + +. 3: (a ) A dichotomy and its realization by an axis-aligned rect­ angle. (b) and (c) Dichotomies unrealizable b y axis-aligned rectangles.

M}, Copyrighted Material 39 Occam's Razor and the sets in T form a cover o f U: Ut=U. tET We assume, of course, that the enti re collection S is itse lf a cover. For any instance S of the Set Cover Problem, we let opt(S) de no te the number of sets in a minimum cardinality cover. Finding an optimal cover is a well-known NP-hard problem. However, is an efficient greedy heuristic that is guaranteed to find a cover 'R of c ardin ality at mos t O(opt(S) lo g m . there ) The greedy heuristic initializes 'R to be the empty colle ctio n.

Is that � E A if and only if 80 is consistent with some concept c E C. The noti on of a concept being consistent w ith a sample will recur frequently in our studies. Definition 3 Let S = {(Xl! b1), ... , (xm, bm)} be any labeled set oj in­ stances, where each Xi E X and each bi E {O, 1}. Let c be a concept over X. Then we say that c is consistent with 8 (or equivalently, 8 is consistent with c) if for aliI::; i ::; m, C(Xi) = bi. Before detailing our choice for the NP-complete language A and the mapping of � to So, just suppose for now that we have managed to arrange things so that a E A if and only if 80 is consistent with some con cept in C.

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