论文标题
永久图
Permanental Graphs
论文作者
论文摘要
一系列发行序列$（p_n）$的无限交换性的两个组件是（i）一致性，（ii）每个$ n $的有限交换性。 Aldous-hoover定理的结果是，任何可分类的，子选择一致的分布序列描述了随机演变的网络都会产生一系列随机图的序列，其预期的边缘数量在节点数量中二次增长。在本说明中，考虑了另一个一致性的概念，即删除和说明的一致性；它是由中国餐厅流程（CRP）定义的无限可交换排列的感觉。一个目标是利用删除和修复的一致性，以在图形$（p_n）上获得非平凡的分布序列，该$（p_n）$稀疏，可交换且与Delete-and-Repair有关，这是一个众所周知的示例，是ewens permutuctations \ cite \ cite \ cite {tavare}。介绍了使用$α$加权的永久性的CRP $（α）$作为在有向图上的分布的概括，以及相应的归一化常量和程度分布；它被称为永久图模型（PGM）。获得负面结果：PGM中没有参数的设置允许在子选择或删除和更改的意义上允许一致的序列$（p_n）$。
The two components for infinite exchangeability of a sequence of distributions $(P_n)$ are (i) consistency, and (ii) finite exchangeability for each $n$. A consequence of the Aldous-Hoover theorem is that any node-exchangeable, subselection-consistent sequence of distributions that describes a randomly evolving network yields a sequence of random graphs whose expected number of edges grows quadratically in the number of nodes. In this note, another notion of consistency is considered, namely, delete-and-repair consistency; it is motivated by the sense in which infinitely exchangeable permutations defined by the Chinese restaurant process (CRP) are consistent. A goal is to exploit delete-and-repair consistency to obtain a nontrivial sequence of distributions on graphs $(P_n)$ that is sparse, exchangeable, and consistent with respect to delete-and-repair, a well known example being the Ewens permutations \cite{tavare}. A generalization of the CRP$(α)$ as a distribution on a directed graph using the $α$-weighted permanent is presented along with the corresponding normalization constant and degree distribution; it is dubbed the Permanental Graph Model (PGM). A negative result is obtained: no setting of parameters in the PGM allows for a consistent sequence $(P_n)$ in the sense of either subselection or delete-and-repair.
