Download Algorithmic Learning Theory: 23rd International Conference, by Nader H. Bshouty, Gilles Stoltz, Nicolas Vayatis, Thomas PDF

By Nader H. Bshouty, Gilles Stoltz, Nicolas Vayatis, Thomas Zeugmann

This ebook constitutes the refereed complaints of the twenty third foreign convention on Algorithmic studying conception, ALT 2012, held in Lyon, France, in October 2012. The convention was once co-located and held in parallel with the fifteenth overseas convention on Discovery technological know-how, DS 2012. The 23 complete papers and five invited talks provided have been rigorously reviewed and chosen from forty seven submissions. The papers are equipped in topical sections on inductive inference, educating and PAC studying, statistical studying thought and class, family members among versions and knowledge, bandit difficulties, on-line prediction of person sequences, and different versions of on-line learning.

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Extra info for Algorithmic Learning Theory: 23rd International Conference, ALT 2012, Lyon, France, October 29-31, 2012. Proceedings

Example text

Proposition 12 (Case and Fulk [4]). If I is either Ex or BC, f ∈ R and S is I-learnable, then S ∪ {f } is I-learnable. Theorem 13. Suppose I is either Ex or BC. Suppose S ∈ WConf Rel. Then S is constructively I-unionable. 44 S. Jain, T. K¨ otzing, and F. Stephan Proof. Suppose S ∈ WConf Rel as witnessed by M ∈ R. Let h be a recursive function such that Mh(i) behaves as follows. Let Mi be obtained effectively from i such that Mi is total and I(Mi ) = I(Mi ). , then Mh(i) (σ) = Mi (σ). Otherwise, Mh(i) (σ) = M (σ).

A class S is said to be dense if [S] = [R]. A class S is everywhere sparse iff for all τ ∈ Seq, there exists a τ τ such that τ ∈ [S]. A total function f is an accumulation point of S iff there exist pairwise distinct functions g0 , g1 , . . in S such that, for all n ∈ N, f [n] gn . }. We let M , N and P range over learners and let C range over classes of learners. Let M0 , M1 , . . denote an acceptable numbering of all the learners. We say that M converges on function f to i (written: M (f )↓ = i) iff for all but finitely many n, M (f [n]) = i.

B) We say that S is I-learnable iff there exists a learner M which I-learns S. (c) I = {S | ∃M [S ⊆ I(M )]}. Enlarging Learnable Classes 41 Definition 3. (a) [10] We say that M is confident iff (i) M is total and (ii) for all total f , M (f )↓ or for all but finitely many n, M (f [n]) =?. (b) We say that M is weakly confident iff (i) M is total and (ii) for all f ∈ R, M (f )↓ or for all but finitely many n, M (f [n]) =?. (c) [2, 9] We say that M is reliable iff (i) M is total and (ii) for all total f , M (f )↓ implies M Ex-learns f .

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