# Granger Causality using Neural Networks

arXiv: https://arxiv.org/abs/2208.03703 · HTML: https://mlsanity.com/paper/2208.03703/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 67 references that are in the map.
- First posted on arXiv 7 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting](https://mlsanity.com/paper/1707.01926/) (2017)
- [Long-term Forecasting using Higher Order Tensor RNNs](https://mlsanity.com/paper/1711.00073/) (2017)
- [In reply to Faes et al. and Barnett et al. regarding "A study of problems encountered in Granger causality analysis from a neuroscience perspective"](https://mlsanity.com/paper/1709.10248/) (2017)
- [High Dimensional Forecasting via Interpretable Vector Autoregression](https://mlsanity.com/paper/1412.5250/) (2014)
- [Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction](https://mlsanity.com/paper/1806.00685/) (2018)
- [Granger Causality Networks for Categorical Time Series](https://mlsanity.com/paper/1706.02781/) (2017)

## Built on by (most cited first, 2 of 2)

- [Nonlinear Permuted Granger Causality](https://mlsanity.com/paper/2308.06220/) (2023)
- [Distributed Dynamic Invariant Causal Prediction in Environmental Time Series](https://mlsanity.com/paper/2603.02902/) (2026)

## Abstract (arXiv)

Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time series data is via Granger Causality (GC). Standard traditional approaches to GC estimation / inference commonly assume linear dynamics, however such simplification does not hold in many real-world applications where signals are inherently non-linear. In such cases, imposing linear models such as vector autoregressive (VAR) models can lead to mis-characterization of true Granger Causal interactions. To overcome this limitation, Tank et al (IEEE Transactions on Pattern Analysis and Machine Learning, 2022) proposed a solution that uses neural networks with sparse regularization penalties. The regularization encourages learnable weights to be sparse, which enables inference on GC. This paper overcomes the limitations of current methods by leveraging advances in machine learning and deep learning which have been demonstrated to learn hidden patterns in the data. We propose novel classes of models that can handle underlying non-linearity in a computationally efficient manner, simultaneously providing GC and lag order selection. Firstly, we present the Learned Kernel VAR (LeKVAR) model that learns kernel parameterized by a shared neural net followed by penalization on learnable weights to discover GC structure. Secondly, we show one can directly decouple lags and individual time series importance via decoupled penalties. This is important as we want to select the lag order during the process of GC estimation. This decoupling acts as a filtering and can be extended to any DL model including Multi-Layer Perceptrons (MLP), Recurrent Neural Networks (RNN), Long Short Term Memory Networks (LSTM), Transformers etc, for simultaneous GC estimation and lag selection.