Structure Learning of Undirected Graphical Models for Count Data

Mainly motivated by the problem of modelling biological processes underlying the basic functions of a cell -that typically involve complex interactions between genes- we present a new algorithm, called PC-LPGM, for learning the structure of undirected graphical models over discrete variables. We prove theoretical consistency of PC-LPGM in the limit of infinite observations and discuss its robustness to model misspecification. To evaluate the performance of PC-LPGM in recovering the true structure of the graphs in situations where relatively moderate sample sizes are available, extensive simulation studies are conducted, that also allow to compare our proposal with its main competitors. A biological validation of the algorithm is presented through the analysis of two real data sets.

Automated summary

Motivated by the complex interactions between genes in modeling biological processes, a new algorithm called PC-LPGM is proposed to learn the structure of undirected graphical models over discrete variables. The theoretical consistency of PC-LPGM and its robustness to model misspecification are proven, with extensive simulation studies and biological validation confirming its performance in recovering true graph structures.