Sparsistent filtering of comovement networks from high-dimensional data

Network representation of large dimensional complex systems has become a standard methodology to delineate the nature of linkages across a large number of constituent entities comprising the systems [33]. Examples range across systems varying widely in terms of nature and architecture: economic and financial networks [9, 5], social networks [44], biological networks like food webs [45], technological networks like world wide web [20] and transportation networks [40] among many others. Broadly speaking, there are two major strands of literature that starts from the analysis of the realized network. One strand of the literature utilizes networks to explore dynamics on it [32], using the realized network as the true representation of the linkages. The other literature goes backward to extract true linkages from the realized linkages [4, 36], maintaining the idea that some of the realized linkages in fact might be spurious. We are interested in the second stream of literature where the fundamental objective is to isolate and filter the key subnetwork out of a large dimensional realized network.