Abstract This article deals with nonobserved dyads during the sampling of a network and consecutive issues in the inference of the stochastic block model (SBM). We review sampling designs and recover missing at random (MAR) and not missing at random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on integrated classification likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein–protein interaction network), where the interpretations considerably depend on the sampling designs considered. Supplementary materials for this article are available online.

中文翻译：

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来自采样数据的随机块模型的变分推理

摘要 本文处理网络采样期间未观察到的二元组和随机块模型 (SBM) 推理中的连续问题。我们审查抽样设计并恢复 SBM 的随机缺失 (MAR) 和不随机缺失 (NMAR) 条件。我们介绍了变分 EM 算法的变体，用于在各种采样设计（MAR 和 NMAR）下推断 SBM，所有这些都可作为 R 包使用。导出基于综合分类似然的模型选择标准，用于选择块数和抽样设计。我们通过模拟研究了这些算法的准确性和适用范围。我们从人种学（种子循环网络）和生物学（蛋白质-蛋白质相互作用网络）探索了两个现实世界的网络，其中解释在很大程度上取决于所考虑的抽样设计。本文的补充材料可在线获取。