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.

翻译：本文介绍了一种名为mlcausality的新算法及其配套Python库，旨在识别非线性格兰杰因果关系。该算法采用灵活的插件式架构，使研究者能够将任意非线性回归器作为基础预测模型。随后，我针对预测回归器为径向基函数核的核岭回归器时，对mlcausality进行了全面的性能分析。结果表明，采用核岭回归的mlcausality在多种模拟数据集上均取得了具有竞争力的AUC得分。此外，与竞争算法相比，基于核岭回归的mlcausality能够产生校准更为精细的$p$值。这一改进使得mlcausality在使用直观的基于$p$值的阈值准则时，可获得更优的准确率得分。最后，相较于现存的非线性格兰杰因果关系算法，采用核岭回归的mlcausality显著降低了计算时间。事实上，在众多案例中，这种创新方法能在比竞争算法所需时间短一个数量级的计算时间内获得更优的解。