Evans Robin J, Richardson Thomas S
Department of Statistics, University of Washington.
J R Stat Soc Series B Stat Methodol. 2013 Sep 1;75(4):743-768. doi: 10.1111/rssb.12020.
Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.
边际对数线性（MLL）模型为多变量离散数据提供了一种灵活的方法。线性约束下的MLL参数化可诱导出各种各样的模型，包括由条件独立性定义的模型。我们引入了一类MLL模型，在通常的全局马尔可夫性质下，这类模型对应于无环有向混合图（ADMG）。我们精确地刻画了对于哪些图，所得的参数化是变分独立的。MLL方法首次根据最少的约束列表对ADMG模型进行了描述。该参数化也很容易适应稀疏建模技术，我们通过几个实际数据示例进行了说明。
