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» Conférences d’après mars 2011 : nouveau site

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Atelier Apprentissage 2005–2006

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Problèmes de classification à coûts asymétriques
Francis Bach (Ecole des mines)

20 février 2006

Receiver Operating Characteristic (ROC) curves are a standard way to display the performance of a set of binary classifiers for all feasible ratios of the costs associated with false positives and false negatives. For linear classifiers, the set of classifiers is typically obtained by training once, holding constant the estimated slope and then varying the intercept to obtain a parameterized set of classifiers whose performances can be plotted in the ROC plane. In this talk, we consider the alternative of varying the asymmetry of the cost function used for training. We show that the ROC curve obtained by varying the intercept and the asymmetry—and hence the slope—always outperforms the ROC curve obtained by varying only the intercept. In addition, we present a path-following algorithm for the support vector machine (SVM) that can compute efficiently the entire ROC curve, that has the same computational properties as training a single classifier. Finally, we provide a theoretical analysis of the relationship between the asymmetric cost model assumed when training a classifier and the cost model assumed in applying the classifier. In particular, we show that the mismatch between the step function used for testing and its convex upper bounds usually used for training leads to a provable and quantifiable difference around extreme asymmetries. Conférence en français

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Francis Bach Francis Bach (Ecole des mines)
Centre de Morphologie Mathématique, Ecole des Mines de Paris