Bounded-Degree Connected Approximations of Stochastic Networks

We propose a method to find optimal sparse connected approximations for large complex networks of nodes interacting over time. Optimality is measured by Kullback-Leibler divergence. The sparsity is controlled by the user through specifying the in-degrees. The approximations have spanning tree subgraphs, enabling them to depict flow through a network. They can also depict feedback. The approximations can capture both significant statistical dependencies in, and preserve salient topological features of, the full (unknown) network. The proposed method can be applied to networks without restrictions on the dynamics beyond stationarity. We analyze computational and sample complexity. We demonstrate their efficacy using a large-scale simulation of the turtle visual cortex and experimental data from the primate motor cortex.