Topology identification of sparse network: A stochastic variational Bayesian approach

Abstract

The topology identification of sparse networks is crucial for network modeling in many fields. The variational Bayesian inference has been proved to be effective for solving this issue. However, since all the observed data are used to compute the posterior distributions of the global variables at each iteration of the classical variational inference, the computation complexity is too high to be suitable for large data sets, especially for large-scale networks, where more data is needed for the inference. In this paper, we derive an efficient algorithm to maximize a lower bound function in the Bayesian inference based on stochastic optimization, where only a part of data is used at each iteration. Compared with the traditional variational Bayesian inference approach, the proposed method can significantly decrease the computation so that it is more suitable for the network identification with large data sets. Several typical sparse networks are used to test the performance of the proposed method, and the results demonstrate its merits.