Fast Block-Sparse Estimation For Vector Networks

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-l0-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.