Download Algorithmic Learning Theory: 27th International Conference, by Ronald Ortner, Hans Ulrich Simon, Sandra Zilles PDF

By Ronald Ortner, Hans Ulrich Simon, Sandra Zilles

ISBN-10: 3319463799

ISBN-13: 9783319463797

This booklet constitutes the refereed court cases of the twenty seventh overseas convention on Algorithmic studying idea, ALT 2016, held in Bari, Italy, in October 2016, co-located with the nineteenth foreign convention on Discovery technological know-how, DS 2016. The 24 normal papers offered during this quantity have been conscientiously reviewed and chosen from forty five submissions. furthermore the booklet comprises five abstracts of invited talks. The papers are prepared in topical sections named: blunders bounds, pattern compression schemes; statistical studying, idea, evolvability; targeted and interactive studying; complexity of educating versions; 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

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Zhivotovskiy and S. Hanneke n Eξ max c ξi p(v)i − p(v)i 4 i=1 ≤ Eξ max v∈V v∈Nγ [0,2γ/c] n = Eξ max c ξi vi − vi + 4 v∈Nγ c ξi vi − vi 4 i=1 ∞ n Eξ k=1 Nγ max [2k γ/c,2k+1 γ/c] c ξi vi − vi 4 i=1 . + 2 log(Mloc (V,γ,n,c)) 1 The first term is upper bounded by by Lemma 1 and by noting cn that |Nγ [0, 2γ/c]|≤M1 (BH (0, (2γ)/c, {X1 , . . , Xn }), (2γ)/2) ≤ Mloc 1 (V, γ, n, c). Now we upper-bound the second term. We start with an arbitrary summand. For any λ > 0, we have n Eξ max v∈{0}∪Nγ [2k γ/c,2k+1 γ/c] ⎛ 1 ⎝ ≤ ln λ c ξi vi − vi 4 i=1 ⎞ n Eξ exp v∈Nγ [2k γ/c,2k+1 γ/c] λc λξi vi − vi 4 i=1 + 1⎠ 1 ≤ ln Nγ 2k γ/c, 2k+1 γ/c exp 2k−2 γ(4λ2 − λc)/c + 1 λ 1 2k+1 exp 2k−2 γ(4λ2 − λc)/c + 1 .

17(81), 1–32 (2016) 17. : Generalization error bounds for stationary autoregressive models (2011). 0942 18. : Generalization error bounds for Bayesian mixture algorithms. J. Mach. Learn. Res. 4, 839–860 (2003) 19. : On learning vector-valued functions. J. Mach. Learn. Res. 6, 615–637 (2005) A Vector-Contraction Inequality for Rademacher Complexities 17 20. : Multiclass learning with simplex coding. In: Advances in Neural Information Processing Systems, pp. 2789–2797 (2012) 21. : The one-sided barrier problem for Gaussian noise.

3) Our complexity term (3) is not worse than the upper bound of Gin´e and Koltchinskii (1) when h is bounded from 0 by a constant. Another interesting property is that the bound (2) involves neither the VC dimension nor the star number explicitly. At the same time one can control the complexity term with both of them from below and above. We should mention that the connection between global covering numbers and VC dimension is well known [11]. Consider the excess loss class GY = {(x, y) → 1[f (x) = y] − 1[f ∗ (x) = y] for f ∈ F} and the class Gf ∗ = {x → 1[f (x) = f ∗ (x)] for f ∈ F}, which may be interpreted as an excess loss class in the realizable case.

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