通过观测性与干预性探测方案可从含潜变量因果结构中获知的一切
Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes
AI总结：
本文刻画含潜变量因果结构在观测与干预探测下的可区分性，证明不可区分等价于共享同一 mDAG，并分析支配关系及探测方案可弱化的限度。
摘要：
在含潜变量的因果结构之间，哪些类型的差异不可能通过探测每个可见变量所获得的统计数据加以区分？如果探测方案只是被动观测，那么众所周知，许多不同的因果结构可以实现相同的联合概率分布。例如，即使在只有两个可见变量的最简单情形中，人们也无法区分一个变量是另一个变量的因果父节点，与这两个变量共享一个潜在共同原因这两种情况。然而，如果我们可以诉诸更强有力的探测方案，例如有可能对其中一个变量进行干预并观测另一个变量，就能够区分这两种因果结构。在本文中，我们探讨的问题是：即便对可见变量采用信息量最大的探测方案，哪些因果结构仍然无法区分。我们发现，两个因果结构保持不可区分，当且仅当它们都与同一个 mDAG 结构（由 Evans（2016）定义）相关联。我们还考虑了一个因果结构何时支配另一个因果结构的问题，这里的支配是指在给定探测方案下，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的特殊情形。）最后，我们研究在多大程度上可以削弱在可见变量上实施的探测方案，同时仍保持与最大信息量探测方案相同的判别能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
