Efficient Learning for Selecting Important Nodes in Random Network

• Published in: IEEE transactions on automatic control 2021-03, Vol.66 (3), p.1321-1328
• Main Authors: Li, Haidong, Xu, Xiaoyun, Peng, Yijie, Chen, Chun-Hung
• Format: Article
• Language: English
• Subjects: Adaptive systems; Approximation; Backstepping; Bayesian learning; dynamic sampling; Interaction parameters; Lyapunov methods; Machine learning; Markov chain; Markov chains; network; Nodes; Nonlinear systems; Parameter sensitivity; ranking and selection (R&S); Sampling; Search engines; Stability analysis; Stochastic processes; Taylor series; Transition probabilities; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.2989753

In this article, we consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the corresponding nodes in a Markov chain defined over the network, as in Google's PageRank. Unlike a deterministic network, the transition probabilities in a random network are unknown but can be estimated by sampling. Under a Bayesian learning framework, we apply the first-order Taylor expansion and normal approximation to provide a computationally efficient posterior approximation of the stationary probabilities. In order to maximize the probability of correct selection, we propose a dynamic sampling procedure, which uses not only posterior means and variances of certain interaction parameters between different nodes, but also the sensitivities of the stationary probabilities with respect to each interaction parameter. Numerical experiment results demonstrate the superiority of the proposed sampling procedure.