Learning from missing data with the Latent Block Model

Gabriel Frisch, Jean-Benoist Leger, Yves Grandvalet

Abstract: Missing data can be informative. Ignoring this information can lead tomisleading conclusions when the data model does not allow informationto be extracted from the missing data. We propose a co-clustering model,based on the Latent Block Model, that aims to take advantage of thisnonignorable nonresponses, also known as Missing Not At Random data(MNAR). A variational expectation-maximization algorithm is derived toperform inference and a model selection criterion is presented. We assessthe proposed approach on a simulation study, before using our model onthe voting records from the lower house of the French Parliament, whereour analysis brings out relevant groups of MPs and texts, together with asensible interpretation of the behavior of non-voters.