Abstract: Latent space models are popular for analyzing dynamic network data. We propose a variational approach to estimate the model parameters and the latent positions of the nodes in the network. The proposed approach is much faster than Markov chain Monte Carlo algorithms, and is able to handle large networks. Theoretical properties of the variational Bayes risk of the proposed procedure are provided. We apply the variational method with the latent space model to simulated and real data to demonstrate its performance.

Key words and phrases: Bayes risk, dynamic network, latent space model, variational inference.