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

By Michael J. Kearns

Emphasizing problems with computational potency, Michael Kearns and Umesh Vazirani introduce a few vital themes in computational studying concept for researchers and scholars in man made intelligence, neural networks, theoretical computing device technological know-how, and statistics.Computational studying conception is a brand new and swiftly increasing region of study that examines formal versions of induction with the pursuits of getting to know the typical tools underlying effective studying algorithms and opting for the computational impediments to learning.Each subject within the ebook has been selected to clarify a normal precept, that's explored in an exact formal surroundings. instinct has been emphasised within the presentation to make the cloth obtainable to the nontheoretician whereas nonetheless supplying specified arguments for the professional. This stability is the results of new proofs of verified theorems, and new shows of the traditional proofs.The subject matters lined comprise the inducement, definitions, and basic effects, either confident and damaging, 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 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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Note that the requirement {3 < 1 is quite weak, since a consistent hy­ pothesis of length O(mn) can always be achieved by simply stori ng the sample S in a table ( at a cost of n + 1 bits per labeled example) and .. giving an arbitrary (say negative) answer for instances that are not in the table. We would certainly not expect such a hypothesis to have any predictive power. Let us also observe that even in the case m < < n, the shortest con­ sistent hypothesis in 1i may in fact be the target concept, and so we must allow size(h) to depend at least linearly on size(c).

1: A 2-decision list and the path followed by an input. 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).

This corresponds with our intuition that as the length of the hy poth esis approaches that of the data itself, the predicti ve power of the hypothesis is diminish ing. 1 in a slightly more general form, in which we measure representational succinctness by the cardinality of the hypothesis class rather than by the bit length size(h}. 1 as a special case. n = Um�l1ln,m. Consider a learni ng algorithm for C using 11. n•m• The following theorem shows that if \ 1ln•m \ is small enough, then the hypothesis outp ut by L has small error with high confidence.

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