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Confidence sets with expected sizes for Multiclass Classification. (arXiv:1608.08783v2 [math.ST] UPDATED)
来源于:arXiv
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 be misleading. We provide in the present
paper a general device that, given an unlabeled dataset and a score function
defined as the minimizer of some empirical and convex risk, outputs a set of
class labels, instead of a single one. Interestingly, this procedure does not
require that the unlabeled dataset explores the whole classes. Even more, the
method is calibrated to control the expected size of the output set while
minimizing the classification risk. We show the statistical optimality of the
procedure and establish rates of convergence under the Tsybakov margin
condition. It turns out that these rates are linear on the number of labels. We
apply our methodology to convex aggregation of confidence sets based on the
V-fold cross validation principle also known as the superlearning principle. We
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