Optimal rate for support vector machine regression with Markov chain samples

Abstract

Support vector machine regression (SVMR) is a regularized learning method in reproducing kernel Hilbert spaces with epsilon-insensitive loss function. Different from the previously known works on the generalization ability of SVMR with independent and identically distributed (i.i.d.) samples, in this paper, we consider the generalization ability of SVMR algorithm based on non-i.i.d. samples, uniformly ergodic Markov chain (u.e.M.c.) samples. We give an error analysis for SVMR algorithm based on u.e.M.c. samples and obtain the optimal learning rate for the SVMR algorithm based on u.e.M.c. samples.