  Graphical models are used in many applications such as medical diagnostic,
computer security, etc. More and more often, the estimation of such models has
to be performed on several predefined strata of the whole population. For
instance, in epidemiology and clinical research, strata are often defined
according to age, gender, treatment or disease type, etc. In this article, we
propose new approaches aimed at estimating binary graphical models on such
strata. Our approaches are obtained by combining well-known methods when
estimating one single binary graphical model, with penalties encouraging
structured sparsity, and which have recently been shown appropriate when
dealing with stratified data. Empirical comparions on synthetic data highlight
that our approaches generally outperform the competitors we considered. An
application is provided where we study associations among injuries suffered by
victims of road accidents according to road user type.
