Nystrom Regularization for Time Series Forecasting

This paper focuses on learning rate analysis of Nystrom regularization with sequential sub-sampling for $\tau$-mixing time series. Using a recently developed Banach-valued Bernstein inequality for $\tau$-mixing sequences and an integral operator approach based on second-order decomposition, we succeed in deriving almost optimal learning rates of Nystrom regularization with sequential sub-sampling for $\tau$-mixing time series. A series of numerical experiments are carried out to verify our theoretical results, showing the excellent learning performance of Nystrom regularization with sequential sub-sampling in learning massive time series data. All these results extend the applicable range of Nystr\"{o}m regularization from i.i.d. samples to non-i.i.d. sequences. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

Authors

• Zirui Sun
• Mingwei Dai
• Yao Wang
• Shao-Bo Lin

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