Fast Block-Sparse Estimation for Vector Networks

Abstract

While there is now a significant literature on sparse inverse covariance estimation, all that literature, with only a couple of exceptions, has dealt only with univariate (or scalar) networks where each node carries a univariate signal. However in many, perhaps most, applications, each node may carry multivariate signals representing multi-attribute data, possibly of different dimensions. Modelling such multivariate (or vector) networks requires fitting block-sparse inverse covariance matrices. Here we achieve maximal block sparsity by maximizing a block-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -sparse penalized likelihood. There is only one previous algorithm that already does this, but it does not scale. Here we address key computational bottlenecks and develop a new algorithm which is much faster and has massively reduced requirements on matrix conditioning. A benchmark study shows a computational speed-up by many orders of magnitude.