The Stochastic Block Model (SBM) is a popular probabilistic model for random graphs. It is commonly used for clustering network data by aggregating nodes that share similar connectivity patterns into blocks. When fitting an SBM to a network which is partially observed, it is important to take into account the underlying process that generates the missing values, otherwise the inference may be biased. This paper introduces missSBM, an R-package fitting the SBM when the network is partially observed, i.e., the adjacency matrix contains not only 1's or 0's encoding presence or absence of edges but also NA's encoding missing information between pairs of nodes. This package implements a set of algorithms for fitting the binary SBM, possibly in the presence of external covariates, by performing variational inference adapted to several observation processes. Our implementation automatically explores different block numbers to select the most relevant model according to the Integrated Classification Likelihood (ICL) criterion. The ICL criterion can also help determine which observation process better corresponds to a given dataset. Finally, missSBM can be used to perform imputation of missing entries in the adjacency matrix. We illustrate the package on a network data set consisting of interactions between political blogs sampled during the French presidential election in 2007.
翻译:软盘块模型(SBM) 是随机图形流行的概率模型。 它通常用于通过将共享类似连接模式的节点汇总到区块中来对网络数据进行分组。 当将磁盘块模型安装到部分观测的网络时, 必须考虑到生成缺失值的基本过程, 否则推论可能会有偏差。 本文引入了 MissSBM, 一个适合 SBM的R包, 当网络部分观测时, 即 匹配矩阵不仅包含 1 或 0 的编码存在或没有边缘, 而且还包含 NA 的对两个节点之间缺少的信息进行编码。 这个软件包使用一套算法来安装二进制 SBM, 可能在外部共变量存在时, 需要考虑产生缺失值, 否则可能是偏差 。 我们的实施会自动探索不同的区块数字, 以选择符合综合分类相似性(ICL) 标准的最相关的模型。 ICL 标准还可以帮助确定哪个观察过程更符合给定的数据集 。 最后, MissSBM 可以在2007年选举时, 在法国选举模型中, 的样本中, 我们将用来在选举中进行选择一个缺少的模型。