  The problem of maximizing the information flow through a sensor network
tasked with an inference objective at the fusion center is considered. The
sensor nodes take observations, compress and send them to the fusion center
through a network of relays. The network imposes capacity constraints on the
rate of transmission in each connection and flow conservation constraints. It
is shown that this rate-constrained inference problem can be cast as a Network
Utility Maximization problem by suitably defining the utility functions for
each sensor, and can be solved using existing techniques. Two practical
settings are analyzed: multi-terminal parameter estimation and binary
hypothesis testing. It is verified via simulations that using the proposed
formulation gives better inference performance than the Max-Flow solution that
simply maximizes the total bit-rate to the fusion center.
