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Structure Learning for Cyclic Linear Causal Models

机译:循环线性因果模型的结构学习

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We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects.We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search.
机译:我们考虑基于观测数据的线性因果模型结构学习问题。我们处理可能的循环混合图给出的模型,从而允许反馈回路和潜在混凝器的影响。在无骨无循环图上概括相关工作,我们假设底层图很简单。这需要任何两个观察到的变量可以通过大多数直接因果效果相关,并且结构方程中的误差术语之间的相关性仅在没有直接因果效果的情况下发生。我们表明,尽管循环中的新微妙之处案例,所认为的简单循环模型是预期的尺寸,并且先前考虑了用于无骨无循环图的分配等效性的标准在循环壳体中具有类似物。我们的结果在模型维度上以特定的基于分数的方法为基于基于分数的方法,用于通过贪婪搜索实现的线性高斯混合图模型的结构学习。

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