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

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