Group Interventions on Deep Networks for Causal Discovery in Subsystems

TL;DR

Causal discovery in multivariate time series often focuses on individual variables, neglecting group-level (subsystem) interactions. The authors propose gCDMI, a deep-learning framework that learns group structure, performs group-level knockoff interventions, and uses model invariance testing to infer causal links between groups. The approach integrates deep autoregressive structure learning (DeepAR), group interventions via knockoffs, and nonparametric invariance testing, augmented by multi-set canonical correlation to manage high-dimensional groups. Across synthetic and real-world domains—including climate-ecosystem, geophysics, and neuroscience—the method shows strong performance, frequently identifying bidirectional group causal relationships and offering valuable insights for complex systems.

Abstract

Causal discovery uncovers complex relationships between variables, enhancing predictions, decision-making, and insights into real-world systems, especially in nonlinear multivariate time series. However, most existing methods primarily focus on pairwise cause-effect relationships, overlooking interactions among groups of variables, i.e., subsystems and their collective causal influence. In this study, we introduce gCDMI, a novel multi-group causal discovery method that leverages group-level interventions on trained deep neural networks and employs model invariance testing to infer causal relationships. Our approach involves three key steps. First, we use deep learning to jointly model the structural relationships among groups of all time series. Second, we apply group-wise interventions to the trained model. Finally, we conduct model invariance testing to determine the presence of causal links among variable groups. We evaluate our method on simulated datasets, demonstrating its superior performance in identifying group-level causal relationships compared to existing methods. Additionally, we validate our approach on real-world datasets, including brain networks and climate ecosystems. Our results highlight that applying group-level interventions to deep learning models, combined with invariance testing, can effectively reveal complex causal structures, offering valuable insights for domains such as neuroscience and climate science.

Figures (12)

• Figure 1: Causal graph of a multivariate system of time series $Z^N = \{Z_i\}_{i=1}^N$ organized into $G = 3$ subsystems $X^G = \{X_i\}_{i=1}^G$, where each subsystem $X_i$ has dimension $D_i$, which sums to the dimension of the whole system $N = \sum_{i=1}^G D_i$.
• Figure 2: A schematic of group causal discovery using deep networks for complex structure learning. Followed by interventions on the trained model. Causal relationship is assessed via model invariance testing by iteratively replacing $X_i$ with a knockoff $\tilde{X}_i$ and evaluating its effect on target group.
• Figure 3: Performance of the methods over variation in interaction density in the synthetically generated multi-groups dataset using SCMs.
• Figure 4: Performance of the methods over increasing nonlinearity in the synthetically generated multi-groups dataset.
• Figure 5: Performance of the methods over increasing number of groups in the synthetically generated multi-groups dataset.

Theorems & Definitions (2)

• Definition 1: Group Causality
• Definition 2: Environment