论文标题
最高线性图形模型，具有及时锦标赛树木的重尾因子
Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments
论文作者
论文摘要
具有重尾因子的图形模型可用于模拟极端事件之间的极端依赖性或因果关系。在贝叶斯网络中，根据父母的指示无环图（DAG），将变量递归定义。我们专注于有关特殊类型的图形的最大线性图形模型，我们称之为及时的锦标赛树。后者是在树状结构中组合的块图，一个有限数量的及每个赛事，每个锦标赛都是连接每个两个节点的DAG。我们在给定变量超过高阈值的情况下有条件地研究最大线性模型的关节尾部的极限。在适当的条件下，限制分布涉及将两个变量之间的最短步道分解为独立的增量，从而模仿了马尔可夫随机场的行为。如果某些变量是潜在的，并且仅观察到子向量，我们还对模型参数的可识别性感兴趣。事实证明，在带有潜在变量的节点上的标准下，这些参数可识别，易于检查。
Graphical models with heavy-tailed factors can be used to model extremal dependence or causality between extreme events. In a Bayesian network, variables are recursively defined in terms of their parents according to a directed acyclic graph (DAG). We focus on max-linear graphical models with respect to a special type of graphs, which we call a tree of transitive tournaments. The latter are block graphs combining in a tree-like structure a finite number of transitive tournaments, each of which is a DAG in which every two nodes are connected. We study the limit of the joint tails of the max-linear model conditionally on the event that a given variable exceeds a high threshold. Under a suitable condition, the limiting distribution involves the factorization into independent increments along the shortest trail between two variables, thereby imitating the behavior of a Markov random field. We are also interested in the identifiability of the model parameters in case some variables are latent and only a subvector is observed. It turns out that the parameters are identifiable under a criterion on the nodes carrying the latent variables which is easy and quick to check.
