Structural learning of Gaussian graphical models from microarray data with p larger than n

Abstract

Learning of large-scale networks of interactions from microarray data is an important and challenging problem in bioinformatics. A widely used approach is to assume that the available data constitute a random sample from a multivariate distribution belonging to a Gaussian graphical model. As a consequence, the prime objects of inference are full-order partial correlations which are partial correlations between two variables given the remaining ones. In the context of microarray data the number of variables exceeds the sample size and this precludes the application of traditional structure learning procedures because a sampling version of full-order partial correlations does not exist. In this paper we introduce a structure learning procedure, that we call the qp-procedure, based on limited-order partial correlations. The procedure is implemented in a freely available package for the statistical software R.