Nyström Regularization for Time Series Forecasting

Abstract

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

Tasks

Reproductions