UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems

TL;DR

UnCLe tackles the challenge of learning time-varying causal graphs from nonlinear time series by combining semantic disentanglement with auto-regressive dependency modeling and perturbation-based causal inference. It introduces a scalable two-phase framework using Uncoupler and Recoupler networks plus multi-channel Dependency Matrices to capture evolving inter-variable influences, with post-hoc dynamic and static discovery modes. Empirical results demonstrate strong performance on static and dynamic benchmarks and provide interpretable phase-specific insights in human motion and other real-world data, while ablations corroborate the importance of each component. The work advances dynamic causal discovery by offering a principled, scalable approach with practical applicability, though it acknowledges the need for theoretical identifiability guarantees and careful consideration in high-stakes deployments.

Abstract

Uncovering cause-effect relationships from observational time series is fundamental to understanding complex systems. While many methods infer static causal graphs, real-world systems often exhibit dynamic causality-where relationships evolve over time. Accurately capturing these temporal dynamics requires time-resolved causal graphs. We propose UnCLe, a novel deep learning method for scalable dynamic causal discovery. UnCLe employs a pair of Uncoupler and Recoupler networks to disentangle input time series into semantic representations and learns inter-variable dependencies via auto-regressive Dependency Matrices. It estimates dynamic causal influences by analyzing datapoint-wise prediction errors induced by temporal perturbations. Extensive experiments demonstrate that UnCLe not only outperforms state-of-the-art baselines on static causal discovery benchmarks but, more importantly, exhibits a unique capability to accurately capture and represent evolving temporal causality in both synthetic and real-world dynamic systems (e.g., human motion). UnCLe offers a promising approach for revealing the underlying, time-varying mechanisms of complex phenomena.

Figures (15)

• Figure 1: The UnCLe framework. Training involves reconstruction and prediction using Uncoupler/Recoupler and Dependency Matrices ($\boldsymbol{\Psi}$). Post-hoc analysis uses temporal perturbation for dynamic graphs ($\hat{\mathcal{G}}^{\text{Pert}}$) and aggregation of $\boldsymbol{\Psi}$ for static graphs ($\hat{\mathcal{G}}^{\text{Agg}}$).
• Figure 2: The dynamic causal strengths between $X_t$ and $Y_t$ discovered by UnCLe and GVAR.
• Figure 3: Dynamic causal analysis on a forward jump motion.
• Figure 4: Time efficiency and causal discovery accuracy on Lorenz#1.
• Figure 5: Ablation study on UnCLe's key components.