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Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data

Ziyi Zhang, Shaogang Ren, Xiaoning Qian, Nick Duffield

TL;DR

This work presents a theoretically-grounded method that infers Granger causal structure and identifies unknown targets by leveraging heterogeneous interventional time series data and illustrates that learning Granger causal structure and recovering interventional targets can mutually promote each other.

Abstract

Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural network prediction models. To alleviate challenges in better deciphering causal structures unambiguously from time series, the use of interventional data has become a practical approach. However, existing methods have yet to be explored in the context of imperfect interventions with unknown targets, which are more common and often more beneficial in a wide range of real-world applications. Additionally, the identifiability issues of Granger causality with unknown interventional targets in complex network models remain unsolved. Our work presents a theoretically-grounded method that infers Granger causal structure and identifies unknown targets by leveraging heterogeneous interventional time series data. We further illustrate that learning Granger causal structure and recovering interventional targets can mutually promote each other. Comparative experiments demonstrate that our method outperforms several robust baseline methods in learning Granger causal structure from interventional time series data.

Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data

TL;DR

This work presents a theoretically-grounded method that infers Granger causal structure and identifies unknown targets by leveraging heterogeneous interventional time series data and illustrates that learning Granger causal structure and recovering interventional targets can mutually promote each other.

Abstract

Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural network prediction models. To alleviate challenges in better deciphering causal structures unambiguously from time series, the use of interventional data has become a practical approach. However, existing methods have yet to be explored in the context of imperfect interventions with unknown targets, which are more common and often more beneficial in a wide range of real-world applications. Additionally, the identifiability issues of Granger causality with unknown interventional targets in complex network models remain unsolved. Our work presents a theoretically-grounded method that infers Granger causal structure and identifies unknown targets by leveraging heterogeneous interventional time series data. We further illustrate that learning Granger causal structure and recovering interventional targets can mutually promote each other. Comparative experiments demonstrate that our method outperforms several robust baseline methods in learning Granger causal structure from interventional time series data.
Paper Structure (16 sections, 2 theorems, 32 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 16 sections, 2 theorems, 32 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Interventional Granger Causal Structure Learning
  5. Granger Causality with Interventions
  6. Non-linear Granger Causality with Interventions
  7. Model Architecture
  8. Optimizing the Penalized Objective
  9. Identifiability
  10. Experiments
  11. Granger Causal Structure Learning
  12. Interventional Family Recovery
  13. Conclusion
  14. Appendix
  15. Proximal Gradient Descent Updates
  16. ...and 1 more sections

Key Result

Theorem 5.1

Let $\hat{\mathcal{G}} \in \mathcal{D}$ be a DAG and $\hat{\mathcal{I}}$ be an interventional family, which $(\hat{\mathcal{G}}, \hat{\mathcal{I}}) \in \mathop{\mathrm{arg\,max}}\limits_{\mathcal{G},\mathcal{I}}\mathcal{S}(\mathcal{G},\mathcal{I})$. Under the assumption that the density models have

Figures (7)

  • Figure 1: Intervention types on time series: With known interventional target (red nodes), altered all causal relationships from parent nodes in imperfect interventions (red dotted lines) versus disconnection from parent nodes in perfect interventions.
  • Figure 2: (Left): Existing methods (node-level imperfect intervention on an unknown target) can only identify the exact node(s); (Right): whereas our method (edge-level intervention identification) can identify both the node(s) and exact edge(s).
  • Figure 3: The information flow in various environments is represented by different colors. During the learning process, the prediction network (P) generates data for the next timestep. Information about unknown targets is contained within the intervention networks ($\textbf{I}_e$), and the Granger causal structure is captured within the causal network (C).
  • Figure 4: The complex interactions in time series data (left) lead to a Granger causal structure (right) that is not a strict DAG.
  • Figure 5: SHD results for Linear (left) and Non-linear (right) Synthetic Interventional Time Series Data.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 5.1
  • Corollary 5.2