# Inductive Granger Causal Modeling for Multivariate Time Series

arXiv: https://arxiv.org/abs/2102.05298 · HTML: https://mlsanity.com/paper/2102.05298/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 14 of 14)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictions](https://mlsanity.com/paper/1710.04806/) (2017)
- [The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification](https://mlsanity.com/paper/1503.01161/) (2015)
- [Interpretable and Steerable Sequence Learning via Prototypes](https://mlsanity.com/paper/1907.09728/) (2019)
- [Exploring Interpretable LSTM Neural Networks over Multi-Variable Data](https://mlsanity.com/paper/1905.12034/) (2019)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Granger-causal Attentive Mixtures of Experts: Learning Important Features with Neural Networks](https://mlsanity.com/paper/1802.02195/) (2018)
- [seq2graph: Discovering Dynamic Dependencies from Multivariate Time Series with Multi-level Attention](https://mlsanity.com/paper/1812.04448/) (2018)

## Built on by (most cited first, 8 of 8)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Edge-Cloud Polarization and Collaboration: A Comprehensive Survey for AI](https://mlsanity.com/paper/2111.06061/) (2021)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Causal Inference in Gene Regulatory Networks with GFlowNet: Towards Scalability in Large Systems](https://mlsanity.com/paper/2310.03579/) (2023)
- [CausalMMM: Learning Causal Structure for Marketing Mix Modeling](https://mlsanity.com/paper/2406.16728/) (2024)
- [Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data](https://mlsanity.com/paper/2406.10419/) (2024)
- [GARNN: An Interpretable Graph Attentive Recurrent Neural Network for Predicting Blood Glucose Levels via Multivariate Time Series](https://mlsanity.com/paper/2402.16230/) (2024)
- [Dynamic Sparse Causal-Attention Temporal Networks for Interpretable Causality Discovery in Multivariate Time Series](https://mlsanity.com/paper/2507.09439/) (2025)

## Abstract (arXiv)

Granger causal modeling is an emerging topic that can uncover Granger causal relationship behind multivariate time series data. In many real-world systems, it is common to encounter a large amount of multivariate time series data collected from different individuals with sharing commonalities. However, there are ongoing concerns regarding Granger causality's applicability in such large scale complex scenarios, presenting both challenges and opportunities for Granger causal structure reconstruction. Existing methods usually train a distinct model for each individual, suffering from inefficiency and over-fitting issues. To bridge this gap, we propose an Inductive GRanger cAusal modeling (InGRA) framework for inductive Granger causality learning and common causal structure detection on multivariate time series, which exploits the shared commonalities underlying the different individuals. In particular, we train one global model for individuals with different Granger causal structures through a novel attention mechanism, called prototypical Granger causal attention. The model can detect common causal structures for different individuals and infer Granger causal structures for newly arrived individuals. Extensive experiments, as well as an online A/B test on an E-commercial advertising platform, demonstrate the superior performances of InGRA.