Network inference and community detection, based on covariance matrices, correlations, and test statistics from arbitrary distributions

In this article we propose methodology for inference of binary-valued adjacency matrices from various measures of the strength of association between pairs of network nodes, or more generally pairs of variables. This strength of association can be quantified by sample covariance and correlation matrices, and more generally by test-statistics and hypothesis test p-values from arbitrary distributions. Community detection methods such as block modeling typically require binary-valued adjacency matrices as a starting point. Hence, a main motivation for the methodology we propose is to obtain binary-valued adjacency matrices from such pairwise measures of strength of association between variables. The proposed methodology is applicable to large high-dimensional data sets and is based on computationally efficient algorithms. We illustrate its utility in a range of contexts and data sets.