InvarGC: Invariant Granger Causality for Heterogeneous Interventional Time Series under Latent Confounding

TL;DR

This work tackles the problem of discovering Granger causal graphs from multivariate time series when latent confounders are present and interventions are unknown across heterogeneous environments. It introduces InvarGC, a multi-component framework that learns a shared invariant Granger causal network $W_0$ while modeling environment-specific interventions $W_k$ and latent factors $Z_t$, optimized to enforce invariance and sparsity. The authors prove identifiability results for the Granger graph, latent confounder subspace, and edge-level inspections of interventions under reasonable assumptions, and demonstrate superior performance on synthetic and real-world data compared to state-of-the-art baselines. The approach advances causal discovery in realistic settings, enabling robust domain adaptation, anomaly detection, and time-series forecasting where interventions and hidden drivers are unknown.

Abstract

Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal relationships. Therefore, numerous recent studies have investigated non-linear Granger causality methods, achieving improved performance. However, these methods often rely on two key assumptions: causal sufficiency and known interventional targets. Causal sufficiency assumes the absence of latent confounders, yet their presence can introduce spurious correlations. Moreover, real-world time series data usually come from heterogeneous environments, without prior knowledge of interventions. Therefore, in practice, it is difficult to distinguish intervened environments from non-intervened ones, and even harder to identify which variables or timesteps are affected. To address these challenges, we propose Invariant Granger Causality (InvarGC), which leverages cross-environment heterogeneity to mitigate the effects of latent confounding and to distinguish intervened from non-intervened environments with edge-level granularity, thereby recovering invariant causal relations. In addition, we establish the identifiability under these conditions. Extensive experiments on both synthetic and real-world datasets demonstrate the competitive performance of our approach compared to state-of-the-art methods.

Figures (5)

• Figure 1: (Left): Imperfect intervention alter all causal relations from the parent nodes to the target node, whereas perfect intervention disconnect the target node from its parents; (Right): Node-level intervention apply to all edges, whereas edge-level intervention generalize to any subset.
• Figure 2: InvarGC is composed of latent confounder inference modules, intervention identification network, invariant Granger causal network, and next-timestep embedding and prediction network.
• Figure 3: Ablation study of the latent confounder inference module (LCIM). We compare four settings: (i) w/o LCIM, (ii) w/ LCIM but without regularization, (iii) w/ LCIM with $L$ set to the true number of latent confounders ($L=|Z|$), and (iv) w/ LCIM with $L > |Z|$.
• Figure 4: Recovered Granger causality and intervention identification across three environments.
• Figure 5: Illustration of latent confounding and interventions in synthetic and Conf-TEP data.

Theorems & Definitions (19)

• Theorem 1: Identifiability of Granger Causal Graph
• proof : Proof sketch
• Theorem 2: Identifiability of the Latent Confounder Subspace
• proof : Proof sketch
• Theorem 3: Identifiability of Edge-level Interventions
• proof : Proof sketch
• Corollary 1: Identifiability of Node-level Interventions
• Lemma 1: Blocking Backdoor Paths
• proof
• Lemma 2: Uniqueness of Minimal Invariant Set