Inferring networks from high-dimensional data with mixed variables

Abstract

We present two methodologies to deal with high-dimensional data with mixed variables, the strongly decomposable graphical model and the regression-type graphical model. The first model is used to infer conditional independence graphs. The latter model is applied to compute the relative importance or contribution of each predictor to the response variables. Recently, penalized likelihood approaches have also been proposed to estimate graph structures. In a simulation study, we compare the performance of the strongly decomposable graphical model and the graphical lasso in terms of graph recovering. Five different graph structures are used to simulate the data: the banded graph, the cluster graph, the random graph, the hub graph and the scale-free graph. We assume the graphs are sparse. Our finding, in the simulation study, is that the strongly decomposable graphical model shows, generally, comparable or better performance both in low and high-dimensional case. Finally, we show an application on mixed data.