Meta Koopman Decomposition for Time Series Forecasting Under Distribution Shifts

Binwu Wang, Xu Wang, Pengkun Wang, Yudong Zhang, Zhengyang Zhou, LEI BAI, Yang Wang

Keywords: Time series forecasting, Koopman, temporal distribution shifts

Abstract: Time series forecasting facilitates various real-world applications and has attracted great research interests. In real-world scenarios, time series forecasting models confront a fundamental issue of temporal distribution shifts, i.e., the statistical properties of time series are evolving over time. In this paper, we utilize Koopman theory to address temporal distribution shifts (TDS). Koopman theory states any time series can be mapped into a Koopman space by proper measurement functions and represented by infinite dimensional linear Koopman operator. Therefore, time series under different distributions can be modeled by different Koopman operators. Considering the linearity of Koopman operators, the Koopman operators for representing time series under different distributions can be decomposed as linear combination of a set of Koopman operators, which we termed as meta Koopman operators. We further theoretically show the infinite dimensional Koopman operators can be approximated by finite matrix multiplications and the meta Koopman operators are equivalent to a set of matrices. Based on the analysis, we propose an auto-encoder framework for implementing the meta Koopman decomposition of time series, which is theoretically able to handle TDS. Extensive experiments conducted on four real-world time series datasets demonstrate the superiority of the proposed model on tackling temporal distribution shifts.

Primary Area: general machine learning (i.e., none of the above)

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Submission Number: 4474