The common cause principle for two random variables $A$ and $B$ is examined in the case of causal insufficiency, when their common cause $C$ is known to exist, but only the joint probability of $A$ and $B$ is observed. As a result, $C$ cannot be uniquely identified (the latent confounder problem). We show that the generalized maximum likelihood method can be applied to this situation and allows identification of $C$ that is consistent with the common cause principle. It closely relates to the maximum entropy principle. Investigation of the two binary symmetric variables reveals a non-analytic behavior of conditional probabilities reminiscent of a second-order phase transition. This occurs during the transition from correlation to anti-correlation in the observed probability distribution. The relation between the generalized likelihood approach and alternative methods, such as predictive likelihood and the minimum common cause entropy, is discussed. The consideration of the common cause for three observed variables (and one hidden cause) uncovers causal structures that defy representation through directed acyclic graphs with the Markov condition.

翻译：针对两个随机变量$A$和$B$的共同原因原理，本文考察了因果信息不充分的情形，即已知共同原因$C$存在，但仅能观测到$A$与$B$的联合概率分布。由此导致$C$无法被唯一识别（潜混杂变量问题）。研究表明，广义最大似然方法可适用于此情境，并能识别出符合共同原因原理的$C$。该方法与最大熵原理密切相关。对两个二元对称变量的分析揭示了条件概率中类似二级相变的非解析行为，该行为出现在观测概率分布从相关向反相关过渡的过程中。本文还探讨了广义似然方法与预测似然、最小共同原因熵等替代方法之间的关联。针对三个观测变量（含一个隐藏原因）的共同原因分析，揭示出某些违背马尔可夫条件的有向无环图难以表征的因果结构。