标题： 关于具有潜在变量的因果结构，可以通过观察和干预探查方案学到的一切 显示英文标题

标题： Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes

摘要： 在带有潜变量的因果结构之间，哪些类型的差异无法通过探测每个可见变量所获得的统计数据来区分？如果探测方案仅仅是被动观察，那么众所周知，许多不同的因果结构可以产生相同的联合概率分布。例如，对于两个可见变量的最简单情况，我们无法区分一个变量是否是另一个变量的因果父节点，还是这两个变量共享一个潜变量的共同原因。然而，如果我们能够使用更强大的探测方案（例如干预其中一个变量并观察另一个变量），则可以区分这两种因果结构。在这里，我们探讨即使在对可见变量实施了最具信息量的探测方案的情况下，哪些因果结构仍然无法区分。我们发现，两种因果结构无法区分当且仅当它们都与相同的mDAG结构（如Evans（2016）定义的那样）相关联。我们也考虑了一种因果结构在某种意义上支配另一种因果结构的问题，即在给定的探测方案下，前者能够实现后者所能实现的所有联合概率分布。（因果结构的等价性是相互支配这一概念的特例。）最后，我们研究了可以在多大程度上减弱作用于可见变量上的探测方案，但仍保持与最大信息量探测方案相同的辨别能力。 显示英文摘要

摘要： What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between one variable being a causal parent of the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.