Inference under Missing Data Conditions in the Stochastic Block Model
Timothée Tabouy, Pierre Barbillon, Julien Chiquet · arXiv (Cornell University) · 2017
This paper deals with non-observed edges during the sampling of a network and consecutive issues in the Stochastic Block Model (SBM) inference. We start by defining missing data conditions with latent state spaces and thereby Missing At Random (MAR) and Not Missing At Random (NMAR) conditions when sampling a network generated under an SBM. We then include sampling design properties and knowledge about observed and non-observed edges in the inference: by means of variational approximations of the distributions of the missing and latent variables, we introduce several variants of the variational EM (VEM) algorithm for SBM that deal with various sampling designs (MAR and NMAR). Model selection criteria based on Integrated Classification Likelihood (ICL) are also 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 finally explore two real-world networks from biology (protein-protein interaction network) and ethnology (seed circulation network), where the interpretations considerably change when the missingness is taken into account.