$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting

Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, Chenjuan Guo

Abstract: Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.

Lay Summary:

Most generative models excell at short-tem probabilistic time series forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). We focus on developing an efficient one-step generative model to effectively handle the LPTSF.

Our paper proposes $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.

Application-Driven Machine Learning: This submission is on Application-Driven Machine Learning.

Link To Code: https://github.com/decisionintelligence/K2VAE

Primary Area: Deep Learning->Sequential Models, Time series

Keywords: Time Series Probabilistic Forecasting

Submission Number: 2349