摘要:可交换性假设是采用贝叶斯模型对网络数据建模的重要前提，基于Aldous-Hoover表示理论的可交换图不能生成稀疏网络.实证结果表明，真实世界中的很多复杂网络都具有节点度幂律分布的稀疏特征，基于Kallenberg表示理论的可交换图能够同时满足可交换性和稀疏性.以Caron-Fox模型和Graphex模型为例，对稀疏可交换图建模的相关概念、理论和方法的研究发展进行了综述.首先讨论了随机图、贝叶斯非参数混合模型、可交换表示理论、Poisson点过程、离散非参数先验等理论的研究历程；然后介绍了Caron-Fox模型的表示；进而总结了进行稀疏可交换图的随机模拟所涉及的截断采样和边缘化采样方法；接下来综述了稀疏可交换图模型的后验推理技术；最后对稀疏可交换图建模的最新进展和研究前景做了介绍.



Abstract:Exchangeability is a key to model network data with Bayesian model. The Aldous-Hoover representation theorem based exchangeable graph model can't generate sparse network, while empirical studies of networks indicate that many real-world complex networks have a power-law degree distribution. Kallenberg representation theorem based exchangeable graph model can admit power-law behavior while retaining desirable exchangeability. This article offers an overview of the emerging literature on concept, theory and methods related to the sparse exchangeable graph model with the Caron-Fox model and the Graphex model as examples. First, developments of random graph models, Bayesian non-parametric mixture models, exchangeability representation theorem, Poisson point process, discrete non-parametric prior etc. are discussed. Next, the Caron-Fox model is introduced. Then, simulation of the sparse exchangeable graph model and related methods such as truncated sampler, and marginalized sampler are summarized. In addition, techniques of model posterior inference are viewed. Finally, state-of-the-art and the prospects for development of the sparse exchangeable graph model are demonstrated.



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