  This paper studies large-scale dynamical networks where the current state of
the system is a linear transformation of the previous state, contaminated by a
multivariate Gaussian noise. Examples include stock markets, human brains and
gene regulatory networks. We introduce a transition matrix to describe the
evolution, which can be translated to a directed Granger transition graph, and
use the concentration matrix of the Gaussian noise to capture the second-order
relations between nodes, which can be translated to an undirected conditional
dependence graph. We propose regularizing the two graphs jointly in topology
identification and dynamics estimation. Based on the notion of joint
association graph (JAG), we develop a joint graphical screening and estimation
(JGSE) framework for efficient network learning in big data. In particular, our
method can pre-determine and remove unnecessary edges based on the joint
graphical structure, referred to as JAG screening, and can decompose a large
network into smaller subnetworks in a robust manner, referred to as JAG
decomposition. JAG screening and decomposition can reduce the problem size and
search space for fine estimation at a later stage. Experiments on both
synthetic data and real-world applications show the effectiveness of the
proposed framework in large-scale network topology identification and dynamics
estimation.
