论文标题
稀疏网络和贝叶斯推断的大规范合奏
Grand canonical ensembles of sparse networks and Bayesian inference
论文作者
论文摘要
最大的熵网络合奏在建模稀疏网络拓扑并解决具有挑战性的推理问题方面非常成功。但是，到目前为止，提出的稀疏最大熵网络模型具有固定数量的节点，并且通常不可交换。在这里，我们考虑了稀疏限制中可交换网络的层次模型，即，链接总数与节点总数线性缩放。该方法是宏伟的规范，即网络的节点数量不是先验的：它是有限的，但可以任意大。通过这种方式，大规范网络合奏规定了处理无限稀疏可交换网络的困难，根据Aldous-Hoover定理，这些网络必须消失。该方法可以用给定的学位分布或网络使用具有潜在变量的给定分布的网络。当仅知道由节点子集诱导的子图时，该模型允许对整个网络的网络大小和程度序列（或潜在变量的序列（或可用于网络重建）的程度序列（或潜在变量的序列）。
Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e. with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e. the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.
