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

翻译：我们介绍了一种方法，能够从变量的时间演化数据中检测因果关系。该方法基于距离排名的信息不平衡这一变分方案，通过统计检验推断不同距离测度的相对信息含量。我们检验了在不对底层动力学显式建模且无需计算动态变量概率密度的条件下，通过纳入潜在驱动系统X的信息，是否能改善被驱动系统Y的可预测性。该框架使得即使在仅已知或测量到少数变量的高维系统中也能实现因果检测。在耦合混沌动力学系统的基准测试中，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。我们还展示了该方法可稳健地检测人类脑电图数据中的因果关系。