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

ISBN-10: 3540466495

ISBN-13: 9783540466499

This e-book constitutes the refereed complaints of the seventeenth overseas convention on Algorithmic studying concept, 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 offered 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 computing device studying. They deal with issues corresponding 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 resources for Algorithmic Learning Theory: 17th International Conference, ALT 2006, Barcelona, Spain, October 7-10, 2006. Proceedings

Example text

To obtain this it is sufficient to combine the following facts: – By Lemma 8, for every non-trivial index i of f , Li has fixed cardinality = Lmax . Therefore GHS could be invoked over the restriction of f onto the grid, f |S , without any trouble. – If f is s-Majority of r-Parity of basic b-literals, then the function obtained by restricting it onto the grid: f |S could be expressed as t-Majority of uParity of basic L-literals where t ≤ s, u ≤ r and L ≤ O(κ ) (due to the 1st property of the refinement).

Hs (x) = 0 for all x. Then for any distribution D over [b]n there is some hi such that |ED [f hi ]| ≥ 1/s. 3 The Generalized Harmonic Sieve Algorithm In this section our goal is to describe a variant of Jackson’s Harmonic Sieve Algorithm and show that under suitable conditions it can efficiently learn certain functions f : [b]n → {−1, 1}. As mentioned earlier, our aim is to attain poly(log b) runtime dependence on b and consequently obtain efficient algorithms as described in Section 2. This goal precludes using Jackson’s original Harmonic Sieve variant for [b]n since the runtime of his weak learner depends polynomially rather than polylogarithmically on b (see [13, Lemma 15]).

Maria Isabel Gonz´ ales Vasco and Igor E. Shparlinski. On the security of Diffie– Hellman bits. In Proceedings of the Workshop on Cryptography and Computational Number Theory, pages 331–342, 2000. 16. Ke Yang. On learning correlated boolean functions using statistical query. In Proceedings of the 12th International Conference on Algorithmic Learning Theory, pages 59–76, 2001. 17. Ke Yang. New lower bounds for statistical query learning. In Proceedings of the 15th Annual Conferene on Computational Learning Theory, pages 229–243, 2002.

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Algorithmic Learning Theory: 17th International Conference, ALT 2006, Barcelona, Spain, October 7-10, 2006. Proceedings by José L. Balcázar, Philip M. Long, Frank Stephan

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