Download Algorithmic Learning Theory: 19th International Conference, by Imre Csiszár (auth.), Yoav Freund, László Györfi, György PDF

By Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)

This booklet constitutes the refereed court cases of the nineteenth overseas convention on Algorithmic studying concept, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the eleventh foreign convention on Discovery technology, DS 2008.

The 31 revised complete papers offered including the abstracts of five invited talks have been rigorously reviewed and chosen from forty six submissions. The papers are devoted to the theoretical foundations of computing device studying; they deal with themes comparable to statistical studying; chance and stochastic strategies; boosting and specialists; energetic and question studying; and inductive inference.

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Extra resources for Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings

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Journal of Machine Learning Research 2, 499–526 (2002) 18. : Learning in Neural Networks: Theoretical Foundations. Cambridge University Press, Cambridge (1999) 19. : Stability and generalization of bipartite ranking algorithms. In: Proceedings of the 18th Annual Conference on Learning Theory (2005) 20. : Covering number bounds of certain regularized linear function classes. Journal of Machine Learning Research 2, 527–550 (2002) 21. : Statistical behavior and consistency of classification methods based on convex risk minimization.

We omit the proof, which follows the proofs of similar results for classification/regression and ranking in [17,19]. Theorem 6 (Stability bound for (f, b)-learners). Let A be an ordinal regression algorithm which, given as input a training sample S ∈ (X × [r])m , learns a real-valued function fS : X→R and a threshold vector bS ≡ (b1S , . . , br−1 S ), and returns as output the prediction rule gS ≡ gfS ,bS . Let be any loss function in this setting such that 0 ≤ (fS , bS , (x, y)) ≤ M for all training samples S and all (x, y) ∈ X × [r], and let β : N→R be such that A has loss stability β with respect to .

If we have, in addition that H ∗ has a density which is bounded by below on [0, 1] and that, for any α, Q∗ (α) < 1 − , for some > 0, then: d∞ (s∗ , sn ) → 0 almost surely, as n goes to ∞. Remark 7 (Boundedness of X ). This assumption is a simplification which can be removed at the cost of a longer proof (the core of the argument can be found in [DGL96]). Remark 8 (Complexity assumption). Instead of assuming a finite VC dimension, a weaker assumption on the combinatorial entropy of the class of partitions may be provided (again check [DGL96] for this refinement).

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