Zirui Sun, Mingwei Dai, Yao Wang et al.
This paper focuses on learning rate analysis of Nyström regularization with sequential sub-sampling for $τ$-mixing time series. Using a recently developed Banach-valued Bernstein inequality for $τ$-mixing sequences and an integral operator approach based on second-order decomposition, we succeed in deriving almost optimal learning rates of Nyström regularization with sequential sub-sampling for $τ$-mixing time series. A series of numerical experiments are carried out to verify our theoretical results, showing the excellent learning performance of Nyström regularization with sequential sub-sampling in learning massive time series data. All these results extend the applicable range of Nyström regularization from i.i.d. samples to non-i.i.d. sequences.