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Online learning with samples drawn from non-identical distributions. (English) Zbl 1235.68157
Summary: Learning algorithms are based on samples which are often drawn independently from an identical distribution (i.i.d.). In this paper we consider a different setting with samples drawn according to a non-identical sequence of probability distributions. Each time a sample is drawn from a different distribution. In this setting we investigate a fully online learning algorithm associated with a general convex loss function and a reproducing kernel Hilbert space (RKHS). Error analysis is conducted under the assumption that the sequence of marginal distributions converges polynomially in the dual of a Hölder space. For regression with least square or insensitive loss, learning rates are given in both the RKHS norm and the ${L}^{2}$ norm. For classification with hinge loss and support vector machine $q$-norm loss, rates are explicitly stated with respect to the excess misclassification error.
##### MSC:
 68T05 Learning and adaptive systems 62H30 Classification and discrimination; cluster analysis (statistics) 62G08 Nonparametric regression