By Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)

ISBN-10: 3540879862

ISBN-13: 9783540879862

ISBN-10: 3540879870

ISBN-13: 9783540879879

This booklet constitutes the refereed complaints of the nineteenth overseas convention on Algorithmic studying idea, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the eleventh foreign convention on Discovery technological know-how, DS 2008.

The 31 revised complete papers provided including the abstracts of five invited talks have been conscientiously reviewed and chosen from forty six submissions. The papers are devoted to the theoretical foundations of desktop studying; they tackle subject matters reminiscent of statistical studying; likelihood and stochastic approaches; boosting and specialists; lively and question studying; and inductive inference.

**Read or Download Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings PDF**

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**Additional info for Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings**

**Sample text**

This research was supported in part by NSF award DMS-0732334. Generalization Bounds for Some Ordinal Regression Algorithms 21 References 1. : Generalized Linear Models, 2nd edn. Chapman and Hall, Boca Raton (1989) 2. : Large margin rank boundaries for ordinal regression. In: Advances in Large Margin Classifiers, pp. 115–132. MIT Press, Cambridge (2000) 3. : Prediction of ordinal classes using regression trees. Fundamenta Informaticae 47, 1001–1013 (2001) 4. : A simple approach to ordinal classification.

First, we use the fact that, for any measurable function h, we have: E(h(X) | Y = +1) = 1−p E p η(X) h(X) | Y = −1 1 − η(X) . ∗ We apply this with h(X) = I{X ∈ Rα } − I{X ∈ Rs,α } to get: ROC∗ (α) − ROC(s, α) = Then we add and substract ∗ Rs,α } = P{X ∈ Rα }, we get: ROC∗ (α)−ROC(s, α) = 1−p E p Q∗ (α) 1−Q∗ (α) 1−p p E η(X) h(X) | Y = −1 . 1 − η(X) and using the fact that 1 − α = P{X ∈ η(X) Q∗ (α) − 1 − η(X) 1 − Q∗ (α) h(X) Y = −1 . Approximation of the Optimal ROC Curve 35 We remove the conditioning with respect to Y = −1 and using then conditioning on X, we obtain: ROC∗ (α) − ROC(s, α) = 1 E p η(X) − Q∗ (α) 1 − Q∗ (α) h(X) .

We underline that the 28 S. Cl´emen¸con and N. Vayatis piecewise linear approximation method we describe next is adaptive in the sense that breakpoints are not ﬁxed in advance and strongly depend on the target curve (which suggests that this scheme possibly yields a sharper constant C). It highlights the explicit relationship between the approximation of the optimal ROC curve and the corresponding piecewise constant scoring function. The ranking algorithm proposed in the sequel (Section 4) will appear as a statistical version of this variable knot approximation, where the unknown quantities driving the recursive partitioning will be replaced by their empirical counterparts.

### Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings by Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)

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