Error Analysis of L1-Regularized Support Vector Machine for Beta-Mixing Sequence

Abstract-In this paper, the extension work on the performance of l₁-regularized support vector machine(l₁-svm) from the classical independent and identically distributed input sequence to the stationary β-mixing input sequence is considered. We establish the bound of generalization error for the l₁-mixing stationary sequence. It is interesting that our result is available even the size of the dictionary considered is infinite, which is different from most previous results of l₁-regularized methods. From the established bound of the generalization error of l₁-svm, we develop a sparsity oracle inequality of l₁-svm for β-mixing input sequence. Following the sparsity oracle inequality, the sufficient condition for the consistency of l₁-svm with stationary β-mixing input sequence can be obtained.