By Boi Faltings (auth.), Joaquim Filipe, Ana Fred (eds.)
This publication constitutes the completely refereed post-conference complaints of the 3rd overseas convention on brokers and synthetic Intelligence, ICAART 2011, held in Rome, Italy, in January 2011. The 26 revised complete papers provided including invited paper have been conscientiously reviewed and chosen from 367 submissions. The papers are geared up in topical sections on synthetic intelligence and on agents.
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Extra info for Agents and Artificial Intelligence: Third International Conference, ICAART 2011, Rome, Italy, January, 28-30, 2011. Revised Selected Papers
Example text
0 10 30 50 70 90 110 130 150 170 C R(ωI ) Remp (ωI ) 190 K h∗ Fig. 5. SRM experiments. With I = 300, optimum points reached at: h∗ = 91 (SRM), h = 91 (C), h = 151 (true risk R). With I = 400, optimum points reached at: h∗ = 111 (SRM), h = 131 (C), h = 151 (true risk R). 6 Summary In the paper we take under consideration the probabilistic relationship between two quantities: Vapnik generalization bound V and the result C of an n-fold non-stratified cross-validation. In the literature on the subject of machine learning (and SLT) typically the stated results have a different focus — namely, the relation between the true risk (generalization error) and either of the two quantities V , C separately.
We denote the set of approximating functions (models) in the sense of both classification or regression estimation as: { f (x, ω)}ω∈Ω , where Ω is the domain of parameters of this set of functions, so a fixed ω can be regarded as an index of a specific function in the set. – The risk functional R : { f (x, ω)}ω∈Ω → R ∪ {+∞} is defined as R(ω) = x∈X y∈Y L f (x, ω), y p(x, y) dydx, (1) p(x)p(y|x) where p(x) is the distribution density of input points, p(y|x) is the conditional density of system/phenomenon outputs y given a fixed x.
2I R(ωI ) − Remp (ωI ) ≤ 41 (27) (28) And since, by definition of ωI , Remp (ω0 ) ≥ Remp (ωI ), the (26) follows. Going back to the cross-validation procedure, we notice that in each single fold the measure Remp corresponds by analogy to the measure R in (26) and the measure Remp corresponds by analogy to Remp therein. Obviously R is defined on an infinite and continuous space Z = X × Y , whereas Remp is defined on a discrete and finite sample {z1 , . . , zI }, but still from the perspective of a single cross-validation fold we may view Remp (ωI ) as the “target” minimal probability of misclassification and Remp (ωI ) as the observed relative frequency of misclassification — an estimate of that probability, remember that we take random subsets {z1 , .