Abstract

This article introduces a new class of models for multiple networks. The core idea is to parameterize a distribution on labeled graphs in terms of a Fréchet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fréchet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience. This article has online supplementary materials.

摘要

本文介绍了一类新的多网络模型。核心思想是根据 Fréchet 均值图（取决于用户指定的度量或图距离选择）和控制该分布关于其均值的集中度的参数来参数化标记图上的分布。熵是这种控制的自然参数，从集中在 Fréchet 均值本身上的点质量到给定顶点集上所有图的均匀分布。我们提供了一种分层贝叶斯方法来利用这种结构，以及从结果后验分布中采样的直接策略。最后，我们通过模拟研究和两个多网络数据分析示例证明了我们方法的有效性：一个来自系统生物学，另一个来自神经科学。这篇文章有在线补充材料。