Graphical modeling represents an established methodology for identifying complex dependencies in biological networks, as exemplified in the study of co‐expression, gene regulatory, and protein interaction networks. The available observations often exhibit an intrinsic heterogeneity, which impacts on the network structure through the modification of specific pathways for distinct groups, such as disease subtypes. We propose to infer the resulting multiple graphs jointly in order to benefit from potential similarities across groups; on the other hand our modeling framework is able to accommodate group idiosyncrasies. We consider directed acyclic graphs (DAGs) as network structures, and develop a Bayesian method for structural learning of multiple DAGs. We explicitly account for Markov equivalence of DAGs, and propose a suitable prior on the collection of graph spaces that induces selective borrowing strength across groups. The resulting inference allows in particular to compute the posterior probability of edge inclusion, a useful summary for representing flow directions within the network. Finally, we detail a simulation study addressing the comparative performance of our method, and present an analysis of two protein networks together with a substantive interpretation of our findings.

中文翻译：

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从观测数据贝叶斯学习多个有向网络。

图形建模代表了一种确定生物网络中复杂依赖性的成熟方法，如共表达，基因调控和蛋白质相互作用网络的研究中所举例说明的。可用的观察结果通常表现出内在的异质性，这会通过修改不同群体（例如疾病亚型）的特定途径来影响网络结构。我们建议联合推断所得的多个图，以便受益于各组之间的潜在相似性；另一方面，我们的建模框架能够适应群体特质。我们将有向无环图（DAG）视为网络结构，并开发了用于多个DAG的结构学习的贝叶斯方法。我们明确说明了DAG的马尔可夫等效性，并在图空间的集合上提出一个合适的先验，以诱导跨组的选择性借用强度。所得的推论尤其允许计算边缘包含的后验概率，这是表示网络内流向的有用总结。最后，我们详细介绍了针对我们方法的比较性能的仿真研究，并给出了对两种蛋白质网络的分析以及对我们发现的实质解释。