Multivariate Time Series Forecasting under Hyperbolic Space Hierarchical Constraints

Kaitao Zhang, Yueyi Xu

Keywords: Multivariate Time Series Forecasting, Hyperbolic Representation Learning, Deep Neural Network

TL;DR: We encode time patches, individual channel and multi-channel sequences into a unified hyperbolic representation space to better learn the complex hierarchical relationships of them.

Abstract: Multivariate time series forecasting has experienced a surge in interest recently. However, significant challenges remain in effectively modeling the multi-level dependencies among time points, sequences, and channels. Existing methods often struggle to fully capture the hierarchical relationships between these three aspects or face efficiency issues. To address this, we propose HyperTime: Hyperbolic space hierarchical constraints for multivariate Time series forecasting. This method initially segments the time series into patches and then extracts temporal dependencies to obtain representations for each channel. It subsequently derives interrelationships among multiple channels based on these representations, encoding time patches, individual channels, and multi-channel series into a unified hyperbolic representation space. By imposing hyperbolic hierarchy and entailment constraints on the encoded representations, the method leverages relationships from local to global among the three levels, ensuring sufficient interactions among point, intra- and inter-channel information. We evaluated HyperTime on several commonly used multivariate time series forecasting datasets and compared it with previously top-performing models. The experimental results demonstrate the effectiveness and efficiency of HyperTime, achieving state-of-the-art performance with only linear complexity. This highlights its proficiency in capturing complex temporal dependencies and interrelationships among channels. Our code is included in the supplemental material and will be released open-source.

Primary Area: learning on time series and dynamical systems

Submission Number: 7375