An empirical comparative study of approximate methods for binary graphical models; application to the search of associations among causes of death in French death certificates

Looking for associations among multiple variables is a topical issue in statistics due to the increasing amount of data encountered in biology, medicine and many other domains involving statistical applications. Graphical models have recently gained popularity for this purpose in the statistical literature. Following the ideas of the LASSO procedure designed for the linear regression framework, recent developments dealing with graphical model selection have been based on $\ell_1$-penalization. In the binary case, however, exact inference is generally very slow or even intractable because of the form of the so-called log-partition function. Various approximate methods have recently been proposed in the literature and the main objective of this paper is to compare them. Through an extensive simulation study, we show that a simple modification of a method relying on a Gaussian approximation achieves good performance and is very fast. We present a real application in which we search for associations among causes of death recorded on French death certificates.