Download Algorithmic Learning Theory: 17th International Conference, by José L. Balcázar, Philip M. Long, Frank Stephan PDF

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By José L. Balcázar, Philip M. Long, Frank Stephan

This e-book constitutes the refereed complaints of the seventeenth foreign convention on Algorithmic studying conception, ALT 2006, held in Barcelona, Spain in October 2006, colocated with the ninth overseas convention on Discovery technological know-how, DS 2006.

The 24 revised complete papers awarded including the abstracts of 5 invited papers have been conscientiously reviewed and chosen from fifty three submissions. The papers are devoted to the theoretical foundations of laptop studying. They tackle themes akin to question versions, online studying, inductive inference, algorithmic forecasting, boosting, aid vector machines, kernel tools, reinforcement studying, and statistical studying models.

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Additional info for Algorithmic Learning Theory: 17th International Conference, ALT 2006, Barcelona, Spain, October 7-10, 2006. Proceedings

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It is furthermore well-known [6] that the smallest size of a threshold circuit (of the type described above) grows linearly with the smallest dimension that allows for a half-space embedding. 7 Hardness of Learning a “Hidden Number” In the final section, we outline a relation between learning and the concept of bit-security in cryptography. 1 Hidden Number Problem and Bit Security Let p be an n-bit prime, (Zp , +, ·) be the field of integers modulo p, (Z∗p , ·) be the (cyclic) group of prime residuals modulo p, and g be a generator of Z∗p .

5 5 Related Lower Bounds The lower bounds from section 4 are tailored to weak learning in the SQ model. These bounds get trivial when a class is efficiently weakly, but not strongly, learnable. Ke Yang [16, 17] presented a technique that allows to reduce the problem of (better than weakly) learning a class consisting of “(almost) uniformly correlated” concepts to the problem of weakly learning a corresponding class of “(almost) uncorrelated” concepts. To the latter class, the bounds from section 4 do apply.

Xi(Lmax −1) }. Let xi0 < xi1 < · · · < xit−1 and let τi : ZLmax → Li be the translation function such that τi (j) = xij . If Li = Li = {0} then τi is the function simply mapping 0 to 0. 6: Invoke GHS over f |S with accuracy /8. This is done by simulating MEM(f |S (x1 , . . , xn )) with MEM(f (τ1 (x1 ), τ2 (x2 ), . . , τn (xn ))). Let the output of the algorithm be g. 7: Let h be a hypothesis function over [b]n such that h(x1 , . . , xn ) = g(τ1−1 ( x1 ), . . , τn−1 ( xn )) ( xi denotes largest value in Li less than or equal to xi ).

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