Real-world systems are often modelled by sets of equations with exogenous random variables. What can we say about the probabilistic and causal aspects of variables that appear in these equations without explicitly solving for them? We prove that, under a solvability assumption, we can construct a Markov ordering graph that implies conditional independences and a causal ordering graph that encodes the effects of soft and perfect interventions by making use of Simon's causal ordering algorithm. Our results shed new light on discussions in causal discovery about the justification of using graphs to simultaneously represent conditional independences and causal relations in models with feedback.

中文翻译：

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方程组隐含的条件独立性和因果关系

现实世界的系统通常由具有外生随机变量的方程组建模。对于出现在这些方程中的变量的概率和因果方面，我们能说些什么，而没有明确地求解它们？我们证明，在可解性假设下，我们可以构建一个隐含条件独立性的马尔可夫排序图和一个因果排序图，通过利用 Simon 的因果排序算法对软和完美干预的影响进行编码。我们的结果为因果发现中关于使用图同时表示具有反馈的模型中的条件独立性和因果关系的理由的讨论提供了新的思路。