In-network online asynchronous regression over a wireless network

We consider online in-network regression over wireless networks. We model the distributed regression as a least square problem and perform the computation over an overlay computational structure that is identical to the multilayer back-propagation of neural networks. The overlay is aligned to the physical topology of the network. The sources of the explanatory (input) and response (output) variables are assumed distributed. Since the wireless network imposes constraints on the allowable simultaneous transmissions, the updates to the estimates of the regression coefficients are necessarily asynchronous. The scheme is analyzed as a stochastic gradient descent algorithm. We also propose the scheduling scheme which respects wireless constraints and dynamically chooses the message passing sequence to speed up the rate of convergence of algorithm. We demonstrate our algorithm performance via numerical results.