By Boi Faltings (auth.), Joaquim Filipe, Ana Fred (eds.)

ISBN-10: 3642299652

ISBN-13: 9783642299650

ISBN-10: 3642299660

ISBN-13: 9783642299667

This ebook constitutes the completely refereed post-conference lawsuits of the 3rd foreign convention on brokers and synthetic Intelligence, ICAART 2011, held in Rome, Italy, in January 2011. The 26 revised complete papers awarded including invited paper have been conscientiously reviewed and chosen from 367 submissions. The papers are prepared in topical sections on man made intelligence and on agents.

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Additional info for Agents and Artificial Intelligence: Third International Conference, ICAART 2011, Rome, Italy, January, 28-30, 2011. Revised Selected Papers

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ZI } using functions from {Q(z, ω)}ω∈Ω . Then, if we relax the sample the following notions of capacity can be considered: 1. expected value of ln N Ω — Vapnik-Chervonenkis entropy: H Ω (I) = z1 ∈Z ··· zI ∈Z ln N Ω (z1 , . . , zI ) · p(z1 ) · · · p(zI )dz1 · · · dzI , 2. ln of expected value of N Ω — annealed entropy: Ω Hann (I) = ln z1 ∈Z ··· zI ∈Z N Ω (z1 , . . , zI ) · p(z1 ) · · · p(zI )dz1 · · · dzI , 3. ln of supremum of N Ω — growth function GΩ (I) = ln sup N Ω (z1 , . . , zI ). ,zI It has been proved that: GΩ (I) = = ln 2I , ≤ ln ∑hk=0 I k dla I ≤ h; , dla I > h, (43) 46 P.

For each fixed setting of the constants, an experiment with repetitions was performed, during which we measured the cross-validation outcome C after each repetition. The range of these outcomes was then compared to the interval implied by the theorems we proved. 50 P. Kl˛esk Table 1. Details (folds, repetitions) of an exemplary experiment no. 1 no. of expeis riment repetition fold Remp (ωI ) ωI = ωI ? 370 true true true .. 1 1 1 .. 10 10 10 .. 1 2 3 .. 394 .. 352 .. 394 We show the results in two tables 1 and 2.

ZI ) · p(z1 ) · · · p(zI )dz1 · · · dzI , 3. ln of supremum of N Ω — growth function GΩ (I) = ln sup N Ω (z1 , . . , zI ). ,zI It has been proved that: GΩ (I) = = ln 2I , ≤ ln ∑hk=0 I k dla I ≤ h; , dla I > h, (43) 46 P. Kl˛esk where h is the Vapnik–Chervonenkis dimension. It has been shown [2] that H Ω (I) (Jensen) ≤ h Ω Hann (I) ≤ GΩ (I) ≤ ln ∑ k=0 I k ≤ ln h eI h I = h(1 + ln ). (44) h And the right-hand-side of (44) can be suitably inserted in the bounds to replace ln N. We mention that appropriate generalizations from the set of indicator functions (classification) onto sets of real-valued functions (regression estimation) can be found in [2] and are based on the notions of: ε-finite net, set of classifiers for a fixed real-valued f , complete set of classifiers for Ω.

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Agents and Artificial Intelligence: Third International Conference, ICAART 2011, Rome, Italy, January, 28-30, 2011. Revised Selected Papers by Boi Faltings (auth.), Joaquim Filipe, Ana Fred (eds.)


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