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B1175
Title: Size controlled confidence sets for multiclass classification Authors:  Mohamed Hebiri - Université Paris-Est -- Marne-la-Vallée (France) [presenting]
Abstract: Multiclass classification problems such as image annotation can involve a large number of classes. In this context, confusion between classes can occur, and single label classification may fail. We present a general device to build a set of labels, namely a confidence set, instead of a single label classifier. An attractive feature of our scheme is that it is semi-supervised: the construction of the confidence set takes advantage of an unlabeled data set to control its expected size. For the outputted confidence set, we establish non-asymptotic risk bounds under the Tsybakov margin condition that are linear on the number of labels. We also apply our methodology to convex aggregation of confidence sets based on the super- learning principle. We illustrate the numerical performance of the procedure on real data and demonstrate in particular that with moderate expected size, w.r.t. the total number of labels, the procedure provides significant improvement of the classification risk.