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

ISBN-10: 3540466495

ISBN-13: 9783540466499

This e-book constitutes the refereed court cases of the seventeenth overseas convention on Algorithmic studying idea, 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 provided 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 computer studying. They deal with themes akin to question versions, online studying, inductive inference, algorithmic forecasting, boosting, help vector machines, kernel tools, reinforcement studying, and statistical studying models.

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

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

**Sample text**

The HS algorithm works by boosting a Fourier-based weak learning algorithm, which is a modiﬁed version of an earlier algorithm due to Kushilevitz and Mansour [18]. In [13] Jackson also described an extension of the HS algorithm to the domain [b]n . His main result for [b]n is an algorithm that can learn any union of s rectangles over [b]n in poly(sb log log b , n) time; note that this runtime is poly(n, s) if and only if b is Θ(1) (and the runtime is clearly exponential in b for any s). There has also been substantial work on learning various classes of unions of rectangles over [b]n in the more demanding model of exact learning from membership and equivalence queries.

As emphasized by [8], the Hidden Number Problem plays a central role for the bit-security of a variety of cryptosystems (not just systems employing the Diﬃe-Hellman function). 2 Hidden Number Problem and Learning Consider a family B = (Bp ) of binary predicates Bp : Z∗p → {±1}. We say that B distinguishes hidden numbers if there exists a polynomial P (n) such that 9 Note that the security of a collection of bits is easier to show than the security of an individual bit because a predictor for a collection of bits is a more powerful tool for solving the evaluation problem for G than the predictor for only one individual bit of the collection.

The “discriminator lemma” of Hajnal et al. [11] can often be used to assert that the desired weak hypothesis exists: Lemma 2 (The Discriminator Lemma [11]). Let H be a class of ±1-valued functions over [b]n and let f : [b]n → {−1, 1} be expressible as f = Majority(h1 , . . , hs ) where each hi ∈ H and h1 (x) + . . + 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}.

### 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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