核Hilbert空间中的显式Granger因果关系
Explicit Granger causality in kernel Hilbert spaces
摘要：
Granger因果关系（GC）无疑是从观测时间序列中推断因果关系的最广泛使用的方法。基于核方法，已经提出了几种GC的非线性替代方案。我们推广核格兰杰因果关系，考虑变量的交叉关系显式在希尔伯特空间。该框架概括了线性和内核GC方法，并根据Rademacher复杂性提供了更严格的性能界限。我们成功地评估了它在标准动力系统中的性能，以及识别耦合罗斯勒系统中的时间箭头，并被用来揭示厄尔尼诺-南方涛动（ENSO）现象对全球土壤水分的影响。
英文摘要：
Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods, and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled Rössler systems, and is exploited to disclose the El Niño-Southern Oscillation (ENSO) phenomenon footprints on soil moisture globally.
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