Nonlinear Granger Causality using Kernel Ridge Regression

TL;DR

This paper introduces mlcausality, a flexible Python library for detecting nonlinear Granger causality, demonstrating that using kernel ridge regression improves accuracy, calibration, and computational efficiency over existing methods.

Contribution

The paper presents a novel, modular algorithm and Python implementation for nonlinear Granger causality, with a focus on kernel ridge regression for enhanced performance.

Findings

Achieves competitive AUC scores across simulated data

Provides more finely calibrated p-values than rival algorithms

Reduces computation times significantly compared to existing methods

Abstract

I introduce a novel algorithm and accompanying Python library, named mlcausality, designed for the identification of nonlinear Granger causal relationships. This novel algorithm uses a flexible plug-in architecture that enables researchers to employ any nonlinear regressor as the base prediction model. Subsequently, I conduct a comprehensive performance analysis of mlcausality when the prediction regressor is the kernel ridge regressor with the radial basis function kernel. The results demonstrate that mlcausality employing kernel ridge regression achieves competitive AUC scores across a diverse set of simulated data. Furthermore, mlcausality with kernel ridge regression yields more finely calibrated $p$-values in comparison to rival algorithms. This enhancement enables mlcausality to attain superior accuracy scores when using intuitive $p$-value-based thresholding criteria. Finally, mlcausality with the kernel ridge regression exhibits significantly reduced computation times compared to existing nonlinear Granger causality algorithms. In fact, in numerous instances, this innovative approach achieves superior solutions within computational timeframes that are an order of magnitude shorter than those required by competing algorithms.