# Nonlinear Permuted Granger Causality

arXiv: https://arxiv.org/abs/2308.06220 · HTML: https://mlsanity.com/paper/2308.06220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 108 references that are in the map.
- First posted on arXiv 11 Aug 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [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)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [Large-scale nonlinear Granger causality: A data-driven, multivariate approach to recovering directed networks from short time-series data](https://mlsanity.com/paper/2009.04681/) (2020)
- [Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series](https://mlsanity.com/paper/1704.02519/) (2017)
- [Granger Causality using Neural Networks](https://mlsanity.com/paper/2208.03703/) (2022)

## Abstract (arXiv)

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence conditional on a specified model. Adaptation of Granger causality to nonlinear data remains challenging, and many methods apply in-sample tests that do not incorporate out-of-sample predictability, leading to concerns of model overfitting. To allow for out-of-sample comparison, a measure of functional connectivity is explicitly defined using permutations of the covariate set. Artificial neural networks serve as featurizers of the data to approximate any arbitrary, nonlinear relationship, and consistent estimation of the variance for each permutation is shown under certain conditions on the featurization process and the model residuals. Performance of the permutation method is compared to penalized variable selection, naive replacement, and omission techniques via simulation, and it is applied to neuronal responses of acoustic stimuli in the auditory cortex of anesthetized rats. Targeted use of the Granger causal framework, when prior knowledge of the causal mechanisms in a dataset are limited, can help to reveal potential predictive relationships between sets of variables that warrant further study.