Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data

TL;DR

This work tackles identifying non-linear, long-range Granger causal relations in multivariate time series by introducing GC-xLSTM, which combines a sparsity-enforcing initial projection with multiple xLSTM forecasters to recover the GC graph $(\mathcal{V},\mathcal{E})$. It contributes a novel reduction loss and proximal optimization that enforce strict input sparsity, enabling robust edge discovery while preserving forecasting performance. The authors provide theoretical discussion on the model’s approximation capabilities and demonstrate superior performance across six diverse datasets (e.g., Lorenz-96, fMRI, Molène, MoCap, and Company Fundamentals) compared with strong baselines, yielding higher accuracy, balanced accuracy, and AUROC. This approach offers scalable, interpretable GC detection in complex time series and has potential for broad applicability in science and industry where understanding temporal interdependencies is critical.

Abstract

Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one time series can predict-Granger cause-future values of another. Although successful, Granger causal methods still struggle with capturing long-range relations between variables. To this end, we leverage the recently successful Extended Long Short-Term Memory (xLSTM) architecture and propose Granger causal xLSTMs (GC-xLSTM). It first enforces sparsity between the time series components by using a novel dynamic loss penalty on the initial projection. Specifically, we adaptively improve the model and identify sparsity candidates. Our joint optimization procedure then ensures that the Granger causal relations are recovered robustly. Our experimental evaluation on six diverse datasets demonstrates the overall efficacy of GC-xLSTM.

Figures (9)

• Figure 1: GC-xLSTM performs three key steps to determine the Granger causal links: Firstly, for each time series component, all variates are embedded with a sparse feature encoder $\bm W$ that is regularized through a novel sparsity loss with learned reduction coefficients $\bm\alpha$. xLSTM models then learn to autoregressively predict future steps from that embedding. Finally, once model estimation is complete, Granger causal dependencies can be extracted from $\bm W$.
• Figure 2: Optimization procedure and compression intuition for GC-xLSTM.
• Figure 3: GC-xLSTM uncovers dynamic GC weather patterns in the Moléne dataset. We observe that the sparsity of the learned Granger causal relations increases with higher $\lambda$.
• Figure 4: GC-xLSTM captures complex human motions. GC-xLSTM is able to uncover complex real-world dependencies in the Human Motion Capture dataset, giving us an intuitive understanding of the learned interactions.
• Figure 5: GC-xLSTM uncovers the vast majority of GC edges. In the highly chaotic $F = 40$ setting of the Lorenz-96 system GC-xLSTM is accurate in predicting the GC edges, shown in dark blue . Errors are marked red .

Theorems & Definitions (1)

• Definition 1: Granger Causality