Algorithmic Learning Theory: 24th International Conference, by Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann

By Sanjay Jain, Rémi Munos, Frank Stephan, Thomas Zeugmann

This e-book constitutes the complaints of the twenty fourth overseas convention on Algorithmic studying concept, ALT 2013, held in Singapore in October 2013, and co-located with the sixteenth overseas convention on Discovery technological know-how, DS 2013. The 23 papers offered during this quantity have been conscientiously reviewed and chosen from 39 submissions. furthermore the e-book comprises three complete papers of invited talks. The papers are geared up in topical sections named: on-line studying, inductive inference and grammatical inference, instructing and studying from queries, bandit conception, statistical studying concept, Bayesian/stochastic studying, and unsupervised/semi-supervised learning.

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Extra resources for Algorithmic Learning Theory: 24th International Conference, ALT 2013, Singapore, October 6-9, 2013. Proceedings

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We summarize the results as in the following theorem. Theorem 5. Let Φ be a separable and strictly convex function over a strictly convex set Γ such that B(f ) ⊆ Γ . Then, there exist algorithms that solve the projection onto B(f ) with respect to ΔΦ and the decomposition for C in time O(n6 + n5 EO), where EO denotes the unit time to evaluate the value of the submodular function f . , the value f (S) depends only on the input size |S|. We believe that with some additional mild assumptions, the projection can also be computed much faster.

There are three important classes that are not studied enough in the literature in the exact learning model: The class of Multiplicity Automata Function, CDNF and Halfspace. A Multiplicity Automata Function (MAF) over the field F is a function of the form: f (x1 , . . , xn ) = A1 (x1 )A2 (x2 ) · · · An (xn ) where each Ai (xi ) is si × si+1 matrix that its entries are univariate polynomials in xi and s1 = sn+1 = 1. In [27] Beimel et al. showed that this class contains all the above classes (in the sense that any function in C of size s has a MAF representation of size poly(s)) except the class of DNF.

22] gives general algorithms for the two procedures, which work efficiently and uniformly for a wide family of concept classes. More precisely, if the convex hull of C is a base polyhedron defined by a submodular function f , then the two procedures can be computed in polynomial time, assuming that f can be evaluated in polynomial time. This result implies that we obtain an essentially one low-regret online algorithm for all concept classes in this family. The family includes the classes of k-sets, permutations, truncated permutations, spanning trees, and more.

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