Online Learning with Samples Drawn from Non-Identical Distributions

Abstract

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 L2 norm. For classification with hinge loss and support vector machine q-norm loss, rates are explicitly stated with respect to the excess misclassification error.