Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based non-parametric approach for inferring the causal relationship between two vector-valued random variables from observational data. Our method employs sparsity estimates of directed and undirected graphs and is based on two new principles for groupwise causal reasoning that we justify theoretically in Pearl's graphical model-based causality framework. Our theoretical considerations are complemented by two new causal discovery algorithms for causal interactions between two random vectors which find the correct causal direction reliably in simulations even if interactions are nonlinear. We evaluate our methods empirically and compare them to other state-of-the-art techniques.
翻译:目前,确定因果关系的方法大多假定变量是标度随机变量。然而,在许多领域,感兴趣的对象是矢量或星度变量组。我们提出了一种新的基于限制的非参数方法,用以从观测数据中推断两个矢量估值随机变量之间的因果关系。我们的方法采用定向和非定向图表的宽度估计,并基于两个关于群集因果推理的新原则,我们从理论上在珍珠的图形模型型因果性框架中证明这种推理是合理的。我们的理论考虑得到两个新的因果发现算法的补充,两个随机矢量之间的因果相互作用,在模拟中找到正确的因果方向,即使互动不是线性。我们用经验来评估我们的方法,并将其与其他最先进的技术进行比较。