By Ronald Ortner, Hans Ulrich Simon, Sandra Zilles

This ebook constitutes the refereed lawsuits of the twenty seventh foreign convention on Algorithmic studying thought, ALT 2016, held in Bari, Italy, in October 2016, co-located with the nineteenth overseas convention on Discovery technology, DS 2016. The 24 typical papers awarded during this quantity have been rigorously reviewed and chosen from forty five submissions. furthermore the e-book comprises five abstracts of invited talks. The papers are equipped in topical sections named: errors bounds, pattern compression schemes; statistical studying, idea, evolvability; specified and interactive studying; complexity of training types; inductive inference; on-line studying; bandits and reinforcement studying; and clustering.

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Extra resources for Algorithmic Learning Theory: 27th International Conference, ALT 2016, Bari, Italy, October 19-21, 2016, Proceedings

Example text

Xn are clear from the context, we sometimes simply write BH (f, γ). We further introduce Mloc 1 (F, γ, n, h) = max max max M1 (BH (f, ε/h, {x1 , . . ,xn f ∈F ε≥γ where M1 (H, ε) denotes the size of a maximal ε-packing of H under ρH distance (for the given x1 , . . , xn points). This quantity measures how one can pack a ball in F by balls of smaller radius. For any h, h ∈ (0, 1], define loc γh,h (n, F) = max{γ ∈ N : hγ ≤ log(Mloc 1 (F, γ, n, h ))}. loc loc When F is clear from the context, we simply write γh,h (n) instead of γh,h (n, F).

We define the growth function SF (n) as the maximum possible number of different classifications of a set of n points realized by classifiers in F. 20 N. Zhivotovskiy and S. Hanneke Definition 1 (Massart and N´ ed´ elec [18]). (P, F) is said to satisfy Massart’s bounded noise condition if f ∗ ∈ F and for some h ∈ [0, 1] it holds |η(X)| ≥ h with probability 1. This constant h is referred to as the margin parameter. For any F, the set of all corresponding distributions satisfying Massart’s bounded noise condition will be denoted by P(h, F).

Theory of classification: a survey of recent advances. ESAIM: Probab. Stat. 9, 323–375 (2005) 5. : A Probabilistic Theory of Pattern Recognition. Applications of Mathematics, vol. 31. Springer, New York (1996) 6. : Concentration inequalities and asymptotic results for ratio type empirical processes. Ann. Probab. 34(3), 1143–1216 (2006) 7. : Theory of disagreement-based active learning. Found. Trends Mach. Learn. 7(2–3), 131–309 (2014) 8. : Minimax analysis of active learning. J. Mach. Learn. Res.

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