Bernstein approximations in glasso‐based estimation of biological networks

Abstract

AbstractThe Gaussian graphical model (GGM) is one of the common dynamic modelling approaches in the construction of gene networks. In inference of this modelling the interaction between genes can be detected mainly via graphical lasso (glasso) or coordinate descent‐based approaches. Although these methods are successful in moderate networks, their performances in accuracy decrease when the system becomes sparser. We here implement a particular type of polynomial transformations, called the Bernstein polynomials, of the network data in advance of their inference to raise the accuracy. From comparative Monte Carlo studies and real data analyses we show that these polynomials are successful in terms of the precision, specificity and F‐measure when the scale‐free networks are modelled via GGM and estimated by glasso, and accordingly they can be used as a preprocessing step in inference of these networks. The Canadian Journal of Statistics 45: 62–76; 2017 © 2017 Statistical Society of Canada