mlsanityData to 7 Oct 2026

Interpretable Models for Granger Causality Using Self-explaining Neural Networks

arXiv 2101.07600 ↗First posted 19 Jan 2021cs.LG stat.MLcited by 44

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Abstract (arXiv)

Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this paper, we propose a novel framework for inferring multivariate Granger causality under nonlinear dynamics based on an extension of self-explaining neural networks. This framework is more interpretable than other neural-network-based techniques for inferring Granger causality, since in addition to relational inference, it also allows detecting signs of Granger-causal effects and inspecting their variability over time. In comprehensive experiments on simulated data, we show that our framework performs on par with several powerful baseline methods at inferring Granger causality and that it achieves better performance at inferring interaction signs. The results suggest that our framework is a viable and more interpretable alternative to sparse-input neural networks for inferring Granger causality.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). Builds on 7 of its 51 references that are in the map. First posted on arXiv 19 Jan 2021.

Builds on

7 of 51 references.

References · 7

  1. 2018Towards Robust Interpretability with Self-Explaining Neural Networkscited by 505
  2. 2018Neural Relational Inference for Interacting Systemscited by 339
  3. 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 99
  4. 2019Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causalitycited by 55
  5. 2018Neural Granger Causalitycited by 19
  6. 2020Discovering Nonlinear Relations with Minimum Predictive Information Regularizationcited by 16
  7. 2015Validity of time reversal for testing Granger causalitycited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 7; 2023: 9; 2024: 7; 2025: 12; 2026: 4.

44 papers.

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  1. 2022Concept Bottleneck Model with Additional Unsupervised Conceptscited by 79
  2. 2023Causal Recurrent Variational Autoencoder for Medical Time Series Generationcited by 44
  3. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  4. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  5. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  6. 2021NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledgecited by 33
  7. 2021Transferable Time-Series Forecasting under Causal Conditional Shiftcited by 18
  8. 2024Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?cited by 17
  9. 2023Interpretation of Time-Series Deep Models: A Surveycited by 15
  10. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  11. 2022Deep Recurrent Modelling of Granger Causality with Latent Confoundingcited by 8
  12. 2022Granger causal inference on DAGs identifies genomic loci regulating transcriptioncited by 8
32 more
  1. 2023Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noisecited by 6
  2. 2021Learning interaction rules from multi-animal trajectories via augmented behavioral modelscited by 5
  3. 2024CausalMMM: Learning Causal Structure for Marketing Mix Modelingcited by 5
  4. 2024Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Datacited by 4
  5. 2025Unifying Explainable Anomaly Detection and Root Cause Analysis in Dynamical Systemscited by 4
  6. 2025ClimateBench-M: A Multi-Modal Climate Data Benchmark with a Simple Generative Methodcited by 4
  7. 2022Granger Causality using Neural Networkscited by 2
  8. 2025UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systemscited by 2
  9. 2022Bayesian Spillover Graphs for Dynamic Networkscited by 1
  10. 2024Bayesian Vector AutoRegression with Factorised Granger-Causal Graphscited by 1
  11. 2024OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and Evaluation Frameworkcited by 1
  12. 2024Detecting Causality in the Frequency Domain with Cross-Mapping Coherencecited by 1
  13. 2025Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Datacited by 1
  14. 2025Time Series Domain Adaptation via Latent Invariant Causal Mechanismcited by 1
  15. 2021An Interpretable Neural Network for Parameter Inferencecited by 0
  16. 2022Jacobian Granger Causal Neural Networks for Analysis of Stationary and Nonstationary Datacited by 0
  17. 2023Nonlinear Permuted Granger Causalitycited by 0
  18. 2023Algorithmic Recourse in Abnormal Multivariate Time Seriescited by 0
  19. 2023Explainable History Distillation by Marked Temporal Point Processcited by 0
  20. 2023News Signals: An NLP Library for Text and Time Seriescited by 0
  21. 2024A VAE-based Framework for Learning Multi-Level Neural Granger-Causal Connectivitycited by 0
  22. 2025Re-examining Granger Causality with Causal Bayesian Networks and Reichenbachs Principlescited by 0
  23. 2025SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Inputcited by 0
  24. 2025Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guaranteescited by 0
  25. 2025Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?cited by 0
  26. 2025Uncovering Causal Relation Shifts in Event Sequences under Out-of-Domain Interventionscited by 0
  27. 2025A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processescited by 0
  28. 2025Learning Granger Causality under Latent Confounding via Intervention-Induced Heterogeneitycited by 0
  29. 2026SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphscited by 0
  30. 2026Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systemscited by 0
  31. 2026Integrating Causal DAGs in Deep RL: Activating Minimal Markovian States with Multi-Order Exposurecited by 0
  32. 2026Time Series Causal Discovery via Context-Conditioned and Causality-Augmented Pretrainingcited by 0