# An Interpretable and Sparse Neural Network Model for Nonlinear Granger Causality Discovery

arXiv: https://arxiv.org/abs/1711.08160 · HTML: https://mlsanity.com/paper/1711.08160/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Embracing the black box: Heading towards foundation models for causal discovery from time series data](https://mlsanity.com/paper/2402.09305/) (2024)
- [Explainable nonlinear modelling of multiple time series with invertible neural networks](https://mlsanity.com/paper/2107.00391/) (2021)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [An Interpretable Neural Network for Parameter Inference](https://mlsanity.com/paper/2106.05536/) (2021)

## Abstract (arXiv)

While most classical approaches to Granger causality detection repose upon linear time series assumptions, many interactions in neuroscience and economics applications are nonlinear. We develop an approach to nonlinear Granger causality detection using multilayer perceptrons where the input to the network is the past time lags of all series and the output is the future value of a single series. A sufficient condition for Granger non-causality in this setting is that all of the outgoing weights of the input data, the past lags of a series, to the first hidden layer are zero. For estimation, we utilize a group lasso penalty to shrink groups of input weights to zero. We also propose a hierarchical penalty for simultaneous Granger causality and lag estimation. We validate our approach on simulated data from both a sparse linear autoregressive model and the sparse and nonlinear Lorenz-96 model.