Empirical Bayes Estimation for the Stochastic Blockmodel
Empirical Bayes Estimation for the Stochastic Blockmodel
复制标题
随机块模型的经验贝叶斯估计
DOI：
10.1214/16-ejs1115
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
C. Priebe
中科院分区：
文献类型：
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作者：
Shakira Suwan;Dominic S. Lee;Runze Tang;D. Sussman;M. Tang;C. Priebe
目前，随机块模型的推理在统计界以及社交网络、引文网络、大脑连接网络（连接组学）等各种应用领域中引起了越来越多的兴趣。最近的理论发展表明，图的谱嵌入可以产生易于处理的分布结果；特别是，随机块模型的随机点积潜在位置图公式为邻接谱嵌入提供了正态分布的混合。我们采用这一新理论提供了一种经验贝叶斯方法，用于估计从随机块模型绘制的随机图中顶点的块成员资格，并证明了其实用性。使用 Metropolis-within-Gibbs 算法进行后验推理。该理论和方法通过随机块模型内外的蒙特卡罗模拟研究进行了说明，并给出了维基百科数据集的实验结果。
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of graphs yields tractable distributional results; in particular, a random dot product latent position graph formulation of the stochastic blockmodel informs a mixture of normal distributions for the adjacency spectral embedding. We employ this new theory to provide an empirical Bayes methodology for estimation of block memberships of vertices in a random graph drawn from the stochastic blockmodel, and demonstrate its practical utility. The posterior inference is conducted using a Metropolis-within-Gibbs algorithm. The theory and methods are illustrated through Monte Carlo simulation studies, both within the stochastic blockmodel and beyond, and experimental results on a Wikipedia data set are presented.