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In many applications concerning statistical graphical models the dataoriginate from several subpopulations that share similarities but have alsosignificant differences. This raises the question of how to estimate severalgraphical models simultaneously. Compiling all the data together to estimate asingle graph would ignore the differences among subpopulations. On the otherhand, estimating a graph from each subpopulation separately does not makeefficient use of the common structure in the data. We develop a new method forsimultaneous estimation of multiple graphical models by estimating thetopological neighborhoods of the involved variables under a sparse inducingpenalty that takes into account the common structure in the subpopulations.Unlike the existing methods for joint graphical models, our method does notrely on spectral decomposition of large matrices, and is therefore morecomputationally attractive for estimating large networks. In addition, wedevelop the asymptotic properties of our method, demonstrate its the numericalcomplexity, and compare it with several existing methods by simulation.Finally, we apply our method to the estimation of genomic networks for a lungcancer dataset which consists of several subpopulations.

Simultaneous Estimation of Graphical Models by Neighborhood Selection