Bayesian structural learning for Latent Class Model with an application to Record Linkage

We consider an extended family of Latent Class models which relaxes the local independence assumption by modeling additional dependencies via graphical models. We propose a Bayesian model averaging procedure to avoid the difficulties of model selection within this family and learn the dependence structure from the data. We show that, by focusing on decomposable dependence graphs, we can design two Gibbs–based MCMC algorithms to sample over the space of eligible models. The procedure is applied on real data on probabilistic Record Linkage.