On the Computation and Applications of Large Dense Partial Correlation Networks

Gaussian graphical models [27] are a popular approach to describing networks, and are directly related to variable prediction via linear regression [20]. The focus is often on graphical model edges described by partial correlations which are zero, identifying pairs of nodes which are conditionally independent [2]. For example, the graphical LASSO [10] imposes a sparse regularization penalty on the precision matrix estimate, seeking a network which trades off predictive accuracy for sparsity. This provides a network which more interpretable and efficient to use, however it is not clear that sparse solutions actually generalize better to new data than dense solutions do [28]. Meanwhile, a different research direction is based on forming edges via some simple relationship such as affinity or univariate correlation. This limited network is used as a starting point for computing sophisticated dense estimates of relatedness between nodes, providing a deeper analysis of network structure. In such research, sparsity is usually imposed on the simple network, however the subsequent analysis is often based on methods which inherently presume Gaussian statistics and l penalties in some sense.