Learning Granger Causality under Latent Confounding via Intervention-Induced Heterogeneity

Abstract

Granger causality characterizes directed predictive dependencies in multivariate time series, but recovering such dependencies becomes challenging in the presence of latent confounding. Cross-environment invariance provides a natural source of information in heterogeneous settings, yet invariance alone can be insufficient: when latent-to-observed mechanisms remain stable, hidden confounders can induce predictive dependencies that are just as invariant as genuine Granger-causal relations. We show that interventions provide an additional source of identifying information by inducing structured variation in observed mechanisms, while stable latent pathways need not exhibit the same cross-environment changes. In practice, however, neither the intervened environments nor the affected mechanisms are known. We propose GRACE, a framework for learning Granger causality under latent confounding from intervention-induced heterogeneity. GRACE decomposes multivariate dynamics into a shared Granger mechanism, sparse environment-specific deviations that capture edge-level interventions, and a latent component that accounts for confounding. Under a linear generative model, we show that GRACE can recover which environments intervene on a given edge when the edge is perturbed in at least one but fewer than half of the environments and the intervention effect is sufficiently large to survive sparsity shrinkage; the recovered intervention pattern then provides a certificate for the corresponding Granger causal edge. Experiments on synthetic and real-world time series demonstrate improved Granger causal structure recovery under latent confounding and unknown interventions.