Learning by Causality to Improve Channel Dependency Modeling in Multivariate Time Series Forecasting

Hyunwook Lee, Hyotaek Jeon, Juwon Kim, Minsik Lee, Ko Keun Kim, Sungahn Ko

Keywords: Multivariate Time Series Forecasting, Channel Dependency, Deep Learning

TL;DR: We propose CALAS, a first end-to-end dynamic causality model that learns both causal strength and time delay for multivariate time series forecasting

Abstract: Beyond the conventional long-term temporal dependency modeling, multivariate time series (MTS) forecasting has rapidly shifted toward channel dependency (CD) modeling. This shift significantly improves modeling quality by fully leveraging both multivariate relationships and temporal dependencies. Recent methods primarily model channel dependency through correlation learning (e.g., crossattention) or non-trainable statistical techniques (e.g., cross-correlation). However, these approaches struggle to fully capture the intrinsic relationships within MTS, particularly those stemming from directed cause-effect (i.e., causality) and nonstationary variates originating from diverse sources. In addition, causality may arise from the signals with different temporal behaviors, such as varying periodicity or discrete event sequences, which is not sufficiently discussed before. In this paper, we propose CALAS (Causality-enhanced Attention with Learnable and Adaptive Spacing), the first end-to-end learning method for MTS forecasting that uncover causality among variates without relying on statistical measures or prior knowledge. To model underlying causality, which consists of causal strength and propagation delay, we newly design a hypernetworks-based 1D convolutions mechanism. Inspired by dilated convolution with learnable spacings (DCLS) and spiking neural networks (SNNs), we extend discrete time delay into a continuous Gaussian kernel. Combining the hypernetworks-generated Gaussian kernel and convolutional weights (i.e., attention or causal strength), we achieve the end-to-end dynamic causality modeling mechanism. This mechanism enhances the model’s ability to capture time-varying causality across multi-source variates, ultimately improving the prediction accuracy, quality, and interpretability. For evaluation, we conduct extensive experiments with six real-world datasets and qualitative analysis to demonstrate CALAS’s superiority in capturing varying causality in a data-agnostic manner. The experiment results indicate that CALAS has significantly improved MTS forecasting accuracy compared to state-of-the-art methods by dynamically modeling causality among variates.

Primary Area: learning on time series and dynamical systems

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Submission Number: 13832