Rademacher Complexity Bounds for Non-I.I.D. Processes

This paper presents the first Rademacher complexity-based error bounds for non-i.i.d. settings, a generalization of similar existing bounds derived for the i.i.d. case. Our bounds hold in the scenario of dependent samples generated by a stationary β-mixing process, which is commonly adopted in many previous studies of non-i.i.d. settings. They benefit from the crucial advantages of Rademacher complexity over other measures of the complexity of hypothesis classes. In particular, they are data-dependent and measure the complexity of a class of hypotheses based on the training sample. The empirical Rademacher complexity can be estimated from such finite samples and lead to tighter generalization bounds. We also present the first margin bounds for kernel-based classification in this non-i.i.d. setting and briefly study their convergence.