Nonlinear Granger Causality using Kernel Ridge Regression
This work addresses the challenge of efficiently detecting nonlinear causal relationships in data for researchers in fields like economics and neuroscience, though it appears incremental as it builds on existing methods with specific improvements.
The paper tackles the problem of identifying nonlinear Granger causal relationships by introducing a novel algorithm and Python library called mlcausality, which uses a flexible plug-in architecture with kernel ridge regression as the base model. The results show that mlcausality achieves competitive AUC scores, more finely calibrated p-values, and significantly reduced computation times, often an order of magnitude faster than existing algorithms.
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.