This article concerns cautious classification models that are allowed to predict a set of class labels or reject make prediction when the uncertainty in is high. set-valued approach equivalent task acceptance region learning, which aims identify subsets input space, each guarantees cover observations with at least predetermined probability. We propose directly learn regions through risk minimiz...

We study whether an asymmetric limited-magnitude ball may tile Z n . This generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes transmitted integer vector bounded number of entries by errors. A construction lattice based on the Hamming metric is given. Several non-existence results are prove...

This paper investigates the asymptotic behavior of soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional numerous data (large n large p with n/p→ δ) drawn from a Gaussian mixture distribution. Sharp predictions classification error rate SVM are provided, as well limits such important parameters margin bias. As further outcome, analysis allows i...