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

ISBN-10: 3540466495

ISBN-13: 9783540466499

This ebook constitutes the refereed lawsuits of the seventeenth foreign convention on Algorithmic studying idea, ALT 2006, held in Barcelona, Spain in October 2006, colocated with the ninth overseas convention on Discovery technology, DS 2006.

The 24 revised complete papers awarded 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 desktop studying. They tackle issues reminiscent of question versions, online studying, inductive inference, algorithmic forecasting, boosting, help vector machines, kernel equipment, reinforcement studying, and statistical studying models.

**Read Online or Download Algorithmic Learning Theory: 17th International Conference, ALT 2006, Barcelona, Spain, October 7-10, 2006. Proceedings PDF**

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

**Example text**

Learning this class has immediate applications for our goal of “learning unions of rectangles”; in particular, it follows that Theorem 2. The concept class of s-Majority of r-rectangles where s = log b) poly(n log b), r = O( loglog(n log(n log b) ) is eﬃciently learnable using GHS. 34 A. A. Servedio This clearly implies eﬃcient learnability for unions (as opposed to majorities) of s such rectangles as well. We then employ a technique of restricting the domain [b]n to a much smaller set and adaptively expanding this set as required.

Since s and bn ·L∞ (D) are both at most poly(τ ) and r = O( loglog(τ log(τ ) ), Lemma 6 implies that there are absolute constants C1 , C2 such that if we consider the kr restrictions ˜1 , . . , ˜r of 1 , . . , r for k = C1 ·τ C2 , we will have E[|hi − j=1 ˜j |] ≤ n 1/(2sb L∞ (D)) where the expectation on the left hand side is with respect to the r uniform distribution on [b]n . This in turn implies that ED [|hi − j=1 ˜j |] ≤ 1/2s. r Let us write h to denote j=1 ˜j . We then have |ED [f h ]| ≥ |ED [f hi ]| − |ED [f (hi − h )]| ≥ |ED [f hi ]| − ED [|f (hi − h )|] = |ED [f hi ]| − ED [|hi − h |] ≥ 1/s − 1/2s = 1/2s.

Poly(n log b)-Majority of O( loglog(n log(n log b) – Unions of poly(log(n log b)) many rectangles with dimension 2 (n log b) ). O( (log log(n loglogb) log log log(n log b))2 – poly(n log b)-Majority of poly(n log b)-Or of disjoint rectangles log b) with dimension O( loglog(n ). log(n log b) Our main algorithmic tool is an extension of Jackson’s boosting- and Fourier-based Harmonic Sieve algorithm [13] to the domain [b]n , building on work of Akavia et al. [1]. Other ingredients used to obtain the results stated above are techniques from exact learning [4] and ideas from recent work on learning augmented AC0 circuits [14] and on representing Boolean functions as thresholds of parities [16].

### 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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