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Journée Mathematical Foundations of Learning Theory

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Asymptotic Properties of Convex Optimization Methods for Multiclass Classification
Peter Bartlett (UC Berkeley)

3 juin 2006

We consider the following pattern classification problem: given a sample of i.i.d. pairs (Xi , Yi ) ∈ X × Y , where Y is finite, find a function f : X → Y that has small misclassification probability. Many successful algorithms for binary classification (with |Y | = 2) involve optimization of a convex criterion. These methods can be generalized in many ways to handle the multiclass case. It turns out that the study of multiclass methods is not a simple extension of results for the binary case. For instance, many apparently natural generalizations of binary methods do not preserve the attractive property of universal consistency (that is, for any probability distribution, the risk of the classifier approaches the best possible). We consider methods that choose a vector-valued function f to optimize a convex criterion of the form

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Peter Bartlett Peter Bartlett (UC Berkeley)