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.

介绍了一种名为 mlcausality 的新算法和伴随的 Python 库，用于识别非线性 Granger 因果关系。通过使用灵活的插件架构，这种新颖的算法使研究人员能够将任何非线性回归器作为基本预测模型。使用径向基函数内核的核岭回归作为预测回归器，对 mlcausality 进行了全面性能分析。结果表明，在各种模拟数据集上，mlcausality 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 可以得到更细致校准的 p 值，从而在使用直观的 p 值阈值准则时获得更高的准确性得分。最后，与现有的非线性 Granger 因果关系算法相比，基于核岭回归的 mlcausality 的计算时间明显缩短。事实上，在许多情况下，这种创新方法在比竞争算法需要更短一个数量级的计算时间内获得更优的解决方案。