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 making assumptions on the underlying dynamics and without the need to compute probability densities of the dynamic variables. 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 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：我们提出一种方法，用于在可获得时间演化数据的情况下检测变量间的因果关系。该方法基于距离等级信息不平衡（一种能够推断不同距离度量间相对信息含量的统计检验）构建变分框架来评估因果关系。我们通过检验是否可通过引入潜在驱动系统X的信息来改善被驱动系统Y的可预测性，且无需假设潜在动力学机制或计算动态变量的概率密度。该框架使得即便在高维系统（仅已知或测量到少数变量）中也能检测因果关系。针对耦合混沌动力系统的基准测试表明，本方法优于其他无模型因果关系检测方法，成功处理了单向与双向耦合。我们还证明该方法可稳健地检测人类脑电图数据中的因果关系。