Deep Learning-based Group Causal Inference in Multivariate Time-series

TL;DR

This work tackles causal direction discovery among groups in nonlinear multivariate time series by combining a deep autoregressive model (DeepAR) to learn group-conditioned distributions with Knockoff-based interventions and model invariance testing. Causality between groups is inferred via a Kolmogorov–Smirnov statistic applied to residuals before and after group-level interventions, enabling detection of both unidirectional and bidirectional links. The approach, gCDMI, demonstrates improved accuracy over Vanilla-PC, Trace, and 2GVecCI on synthetic data and real datasets including FLUXNET, ENSO, and simulated fMRI, albeit with higher computational cost due to deep learning. The method has practical potential for uncovering climate-ecosystem and brain-network causal pathways under nonlinear dynamics, with code available for reproducibility.

Abstract

Causal inference in a nonlinear system of multivariate timeseries is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world complex systems. Causality methods typically identify the causal structure of a multivariate system by considering the cause-effect relationship of each pair of variables while ignoring the collective effect of a group of variables or interactions involving more than two-time series variables. In this work, we test model invariance by group-level interventions on the trained deep networks to infer causal direction in groups of variables, such as climate and ecosystem, brain networks, etc. Extensive testing with synthetic and real-world time series data shows a significant improvement of our method over other applied group causality methods and provides us insights into real-world time series. The code for our method can be found at:https://github.com/wasimahmadpk/gCause.

Figures (4)

• Figure 1: Interactions among groups of multivariate time series data of various dimensions.
• Figure 2: Schematic diagram of group causal discovery method where we model the complex relation among all variables in the system with deep learning approximator. For group-level causal inference, we implement model invariance testing by applying intervention to a group of interest and estimate its influence on the target group.
• Figure 3: Distribution shift of a. ecosystem group $G_{\text{E}} = \{GPP, R_{\text{eco}}\}$ in response to intervention on climate group $G_{\text{C}}= \{T, R_g\}$. b. British Columbia temperature in response to intervention on ENSO temperature data. c. Brain network $N_2$ in fMRI time series after group-level intervention on network $N_1$.
• Figure 4: a. Illustration of exchangeability property $(Z_1, Z_2) \overset{d}{=} (Z_1, \tilde{Z}_2)$ of knockoff variables b. Shows the correlation matrix $\Sigma_{Z\tilde{Z}}$ of the original variables $Z$ and knockoffs $\tilde{Z}$ where the sub-matrix for the correlation within the generated knockoffs $\Sigma_{\tilde{Z}_{1}\tilde{Z}_{2}}$ is similar to that of correlation in original variables $\Sigma_{Z_{1}Z_{2}}$ , enclosed in red squares. While the variable-wise correlation is minimized with their respective knockoff copies, i.e., $\sigma_{Z_{1}\tilde{Z}_{1}}, \sigma_{Z_{2}\tilde{Z}_{2}}\approx 0$, shown in white squares.