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

This booklet constitutes the refereed complaints of the seventeenth foreign convention on Algorithmic studying thought, ALT 2006, held in Barcelona, Spain in October 2006, colocated with the ninth foreign convention on Discovery technology, DS 2006.

The 24 revised complete papers offered including the abstracts of 5 invited papers have been rigorously reviewed and chosen from fifty three submissions. The papers are devoted to the theoretical foundations of computing device studying. They deal with subject matters akin to question versions, online studying, inductive inference, algorithmic forecasting, boosting, aid vector machines, kernel equipment, reinforcement studying, and statistical studying models.

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

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N (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 ). 8: if h -approximates f then 9: Output h and terminate. 10: end if 11: Perform random membership queries until an element (x1 , . . , xn ) ∈ [b]n is found such that f ( x1 , . . , xn ) = f (x1 , . . , xn ). 12: Find an index 1 ≤ i ≤ n such that f ( x1 , . . , xi−1 , xi , .

6. J¨ urgen Forster, Matthias Krause, Satyanarayana V. Lokam, Rustam Mubarakzjanov, Niels Schmitt, and Hans Ulrich Simon. Relations between communication complexity, linear arrangements, and computational complexity. In Proceedings of the 21’st Annual Conference on the Foundations of Software Technology and Theoretical Computer Science, pages 171–182, 2001. 7. Michael Kearns. Efficient noise-tolerant learning from statistical queries. Journal of the Association on Computing Machinery, 45(6):983–1006, 1998.

Then C can be learned in time poly(n, log b, 4 −1 , γ −1 ). Learning Majority of Parity Using GHS In this section we identify classes of functions which can be learned efficiently using the GHS algorithm and prove Theorem 1. To prove Theorem 1, we show that for any concept f ∈ C and under any smooth distribution there must be some Fourier basis element which has nonnegligible correlation with f ; this is the essential step which lets us apply the Generalized Harmonic Sieve. 2. 3 we give an alternate argument which yields a Theorem 1 analogue but with a slightly log b) different bound on r, namely r = O( log(n log log b ).

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