因果期望最大化
Causal Expectation-Maximisation
摘要：
结构因果模型是珀尔因果理论的基本建模单元;原则上，它们允许我们解决反事实，这是因果关系阶梯的最高一级。但它们通常包含潜在变量，限制了它们在特殊环境中的应用。这似乎是一个事实的后果，证明在本文中，因果推理是NP-困难的，即使在模型的特点是多边形图。为了处理这种困难，我们引入因果EM算法。它的主要目的是从分类显式变量的数据中重建潜变量的不确定性。然后通过贝叶斯网络的标准算法来解决反事实推理。其结果是一种近似计算反事实的通用方法，无论它们是否可识别（在这种情况下，我们提供边界）。我们的经验表明，以及通过推导可信的区间，我们提供的近似在相当数量的EM运行变得准确。这些结果导致我们最后认为，似乎有一个未被注意的限制趋势的想法，反事实的界限往往可以计算的结构方程的知识。
英文摘要：
Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit their application to special settings. This appears to be a consequence of the fact, proven in this paper, that causal inference is NP-hard even in models characterised by polytree-shaped graphs. To deal with such a hardness, we introduce the causal EM algorithm. Its primary aim is to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. Counterfactual inference is then addressed via standard algorithms for Bayesian networks. The result is a general method to approximately compute counterfactuals, be they identifiable or not (in which case we deliver bounds). We show empirically, as well as by deriving credible intervals, that the approximation we provide becomes accurate in a fair number of EM runs. These results lead us finally to argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
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