Design of Compressed Sensing Systems via Density-Evolution Framework for Structure Recovery in Graphical Models

It has been shown that the task of learning the structure of Bayesian networks (BN) from observational data is an NP-Hard problem. Although there have been attempts made to tackle this problem, these solutions assume direct access to the observational data which may not be practical in certain applications. In this paper, we explore the feasibility of recovering the structure of Gaussian Bayesian Network (GBN) from compressed (low dimensional and indirect) measurements. We propose a novel density-evolution based framework for optimizing compressed linear measurement systems that would, by design, allow for more accurate retrieval of the covariance matrix and thereby the graph structure. In particular, under the assumption that both the covariance matrix and the graph are sparse, we show that the structure of GBN can indeed be recovered from resulting compressed measurements. The numerical simulations show that our sensing systems outperform the state of the art with respect to Maximum absolute error (MAE) and have comparable performance with respect to precision and recall, without any need for ad-hoc parameter tuning.