Scalable Fault Diagnosis in IP Networks using Graphical Models: A Variational Inference Approach

In this paper we investigate the fault diagnosis problem in IP networks. We provide a lower bound on the average number of probes per edge using variational inference technique proposed in the context of graphical models under noisy probe measurements. To obtain the bounds, we construct a graphical model using Bayesian networks. The advantages of the variational inference technique are the explicit choices of a simplifying conjugate function and a computationally tolerable approximation to address the intractable detection problem for large networks. We propose an entropy lower (EL) bound by drawing similarities between the coding problem over binary symmetric channel and the diagnosis problem and compare it against the variational lower bound. In addition, we discuss scalable and non-scalable scenarios in the presence of noise. Simulation results demonstrate that indeed the variational inference technique can provide a linear growth of the average number of probes per edge as a function of the network size.