We study identifiability of Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are monotone non-decreasing in topological order. This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.

中文翻译：

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AMP 链图模型的可识别性

我们研究了 Andersson-Madigan-Perlman (AMP) 链图模型的可识别性，这是线性结构方程模型和高斯图模型的常见推广。AMP 模型由链组件上的 DAG 描述，链组件本身是无向图。对于已知的链组件分解，我们证明如果链组件的残差协方差矩阵的行列式在拓扑顺序上是单调非递减的，则链组件上的 DAG 是可识别的。该条件扩展了贝叶斯网络的等方差可识别性标准，并且可以从行列式推广到半正定矩阵上的任何超可加函数。当组件分解未知时，我们描述了允许使用基于子模函数最小化的多项式时间算法恢复完整结构的条件。我们还进行了实验，将我们的算法性能与现有基线进行比较。