InvarGC: Invariant Granger Causality for Heterogeneous Interventional Time Series under Latent Confounding
Ziyi Zhang, Shaogang Ren, Xiaoning Qian, Nick Duffield
TL;DR
InvarGC is a novel method for causal discovery in heterogeneous time series data that accounts for latent confounders and unknown interventions, improving accuracy over existing approaches.
Contribution
The paper introduces InvarGC, a new invariant Granger causality method that leverages cross-environment heterogeneity to identify causal relations despite latent confounders and unknown interventions.
Findings
InvarGC outperforms state-of-the-art methods on synthetic datasets.
InvarGC successfully identifies causal edges in real-world data.
The method demonstrates robustness to latent confounding and intervention heterogeneity.
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…
Peer Reviews
Decision·Submitted to ICLR 2026
- Tackles a relevant setting: unknown interventions + latent confounding, and the problem setup is clear. - Identifiability results (graph, latent subspace, edge-level interventions) with explicit assumptions. - Good experimental results vs. strong baselines across synthetic and real data; sensible ablations on $L$.
1. The largest real-world example (TEP) uses 33 variables, and Causal-Rivers uses node subsets. While nontrivial, this leaves open whether InvarGC scales effectively to higher-dimensional (>100 variables), longer sequences, or truly networked time series encountered in domains such as neuroscience, genomics, or industrial process control. No runtime or computational complexity results are reported either. 2. Although the ablation study in Figure 3 analyzes the effect of the number of latent conf
1. The problem is well-formulated and considers a very realistic and under-studied setting. 2. The authors conduct extensive simulations to demonstrate the effectiveness of the proposed algorithm, especially on real-world datasets.
1. The notation is a little bit confusing and hard to follow. For example, the subscript of $W$ includes both numbers and variables. It would be better if it can be unified (say use $W_{0, 1:d}$ instead of $X_{0,X_{t+1}X_t}$). 2. Some of the technical details are not clearly explained, such as mathematical formulation of certain assumptions and technical details (see Q1 and Q4 below). 3. It seems to me that the identification results considers a much simpler setting than the model described in
1. The paper tackles an important gap in the literature by proposing an algorithm that recovers an invariant Granger causal graph under latent confounders and unknown interventions. 2. The paper is well written and logically organized. 3. The work provides both theoretical guarantees and empirical validation. 4. The experimental results show impressive performance, often matching or outperforming the baselines.
1. The theoretical guarantees are not solid. 1.1 Assumption A4 is vague. Combining the main paper and the appendix, “...interventions are sufficiently diverse to distinguish true causal parents from non-parents.” means that, for $X^j_t\in PA(X^i_{t+1})$, that "there exists at least one environment in which the mechanism of the edge $ j \rightarrow i$ differs from its invariant form.", it also means that for any latent variables connected with the target variable, "there exists an environment in
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Taxonomy
TopicsTime Series Analysis and Forecasting · Bayesian Modeling and Causal Inference · Machine Learning in Healthcare