A0541
Title: SANVI: A fast spectral-assisted network variational inference method with an extended surrogate likelihood function
Authors: Dingbo Wu - Indiana University (United States)
Fangzheng Xie - Johns Hopkins University (United States)
Fangzheng Xie - Indiana University (United States) [presenting]
Abstract: Bayesian inference has been broadly applied to statistical network analysis, but suffers from the expensive computational costs due to the nature of Markov chain Monte Carlo sampling algorithms. A novel and computationally efficient spectral-assisted network variational inference (SANVI) method is proposed under the generalized random dot product graph framework. The key idea is a cleverly designed extended surrogate likelihood function that enjoys two convenient features. Firstly, it decouples the generalized inner product of latent positions in the random graph model. Secondly, it extends the domain of the original likelihood function to the entire Euclidean space. Leveraging these features, a computationally efficient Gaussian variational inference algorithm is designed via the stochastic gradient descent method for Bayesian inference of networks. Furthermore, the asymptotic efficiency of the maximum extended surrogate likelihood estimator and the Bernstein-von Mises limit of the variational posterior distribution is shown. Through extensive numerical studies, the practical advantage of the proposed SANVI algorithm compared to the classical Markov chain Monte Carlo algorithm is demonstrated, including the estimation accuracy for the latent positions and the computational costs.
