Compressive Kalman filtering for recovering temporally-rewiring genetic networks

Genetic regulatory networks undergo rewiring over time in response to cellular developments and environmental stimuli. The main challenge in estimating time-varying genetic interactions is the limited number of observations at each time point; thus making the problem unidentifiable. We formulate the recovery of temporally-rewiring genetic networks as a tracking problem, where the target to be tracked over time consists of the set of genetic interactions. We circumvent the observability issue (due to the limited number of measurements) by taking into account the sparsity of genetic networks. With linear dynamics, we use a compressive Kalman filter to track the interactions as they evolve over time. Our simulation results show that the compressive Kalman filter achieves good tracking performance even with one measurement available at each time point; whereas the classical (unconstrained) Kalman filter completely fails in obtaining meaningful tracking.