Vector ℓ0 Sparse Conditional Independence Graphs

Abstract

One of the main approaches to system identification of networks of time series or signals is conditional independence graphical (CIG) modeling. In the Gaussian case, the conditional dependence structure of the nodal time series is determined by the location of zeros in the precision matrix (inverse covariance matrix). And this determines the graph structure of the network. Despite the many applications of CIG models, the theory and algorithms have so far only dealt with networks of univariate or scalar signals. But in most applications the nodes carry multivariate or vector signals. Here we extend CIG modeling to handle such data by posing a group ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> sparse penalised block precision matrix estimation problem. We develop a double cyclic descent algorithm to solve it. And we compare the method with a group ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> penalised alternative in simulations.