The paper was reviewed by three experts in the field. The reviewers and AC all agree that the paper contains novel contributions, but share the same opinion that it could be strengthened by addressing the reviewers' comments. In addition to the reviewers' comments such as the need to adding comparison with VGAE and its variates, the AC would like to provide some additional feedback to the authors: The AC views the paper as some kind of smart combination of edge partition model, gamma belief net, and Dirichlet belief net, enhanced by adding covariate dependence and by incorporate the network information in learning the connection weights of the Dirichlet belief net. Pros: 1) the combination is non-trival: replacing the gamma weights in edge partition model with latent counts is the key to allow closed-form Gibbs sampling (upward latent count propagation followed by downward variable sampling). How the X is used in (3) and sampled in (5) is novel.

The edge partition model (EPM) is a generative model for extracting an overlapping community structure from static graph-structured data. In the EPM, the gamma process (GaP) prior is adopted to infer the appropriate number of latent communities, and each vertex is endowed with a gamma distributed positive memberships vector. Despite having many attractive properties, inference in the EPM is typically performed using Markov chain Monte Carlo (MCMC) methods that prevent it from being applied to massive network data. In this paper, we generalize the EPM to account for dynamic enviroment by representing each vertex with a positive memberships vector constructed using Dirichlet prior specification, and capturing the time-evolving behaviour of vertices via a Dirichlet Markov chain construction. A simple-to-implement Gibbs sampler is proposed to perform posterior computation using Negative- Binomial augmentation technique. For large network data, we propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in the proposed model. The experimental results show that the novel methods achieve competitive performance in terms of link prediction, while being much faster.

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key challenge in either setting is controlling the variance of gradient estimates: recent work has shown that for continuous latent variables, particularly multivariate Gaussians, this can be achieved by using the gradient of the log posterior. In this paper we apply the same idea to gamma distributed latent variables given gamma variational distributions, enabling straightforward "black box" variational inference in models where sparsity and non-negativity are appropriate. We demonstrate the method on a recently proposed gamma process model for network data, as well as a novel sparse factor analysis. We outperform generic sampling algorithms and the approach of using Gaussian variational distributions on transformed variables.