We introduce an approach which allows inferring causal relationships between variables for which the time evolution is available. Our method builds on the ideas of Granger Causality and Transfer Entropy, but overcomes most of their limitations. Specifically, our approach tests whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without making assumptions on the underlying dynamics and without the need to compute probability densities of the dynamic variables. Causality is assessed by a rigorous variational scheme based on the Information Imbalance of distance ranks, a recently developed statistical test capable of inferring the relative information content of different distance measures. This framework makes causality detection possible even for high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings, and it is capable of detecting the arrow of time when present. We also show that the method can be used to robustly detect causality in electroencephalography data in humans.

翻译：我们提出了一种方法，能够从具有时间演变的变量中推断因果关系。该方法基于格兰杰因果关系和转移熵的思想，但克服了它们的大部分局限性。具体而言，我们的方法测试了将潜在驱动系统X的信息纳入后，是否能够提高被假定为受驱动系统Y的可预测性，而无需对底层动力学做出假设，也无需计算动态变量的概率密度。因果关系通过基于距离秩的信息不平衡（一种近期开发的统计检验方法，能够推断不同距离度量的相对信息含量）的严格变分方案进行评估。这一框架使得即使在仅知道或测量到少数变量的高维系统中，也能实现因果检测。对耦合动力系统的基准测试表明，我们的方法优于其他无模型因果检测方法，成功处理了单向和双向耦合，并能检测时间箭头（若存在）。我们还展示了该方法能够稳健地检测人类脑电图数据中的因果关系。