A probabilistic framework based on the covariate-dependent relational gamma process is developed to analyze relational data arising from longitudinal networks. The proposed framework characterizes networked nodes by nonnegative node-group memberships, which allow each node to belong to multiple latent groups simultaneously, and encodes edge probabilities between each pair of nodes using a Bernoulli Poisson link to the embedded latent space. Within the latent space, our framework models the birth and death dynamics of individual groups via a thinning function. Our framework also captures the evolution of individual node-group memberships over time using gamma Markov processes. Exploiting the recent advances in data augmentation and marginalization techniques, a simple and efficient Gibbs sampler is proposed for posterior computation. Experimental results on a simulation study and three real-world temporal network data sets demonstrate the model's capability, competitive performance and scalability compared to state-of-the-art methods.

We propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is based on a stochastic neural network that generates discrete output samples and is trained using the Wasserstein GAN objective. NetGAN is able to produce graphs that exhibit well-known network patterns without explicitly specifying them in the model definition. At the same time, our model exhibits strong generalization properties, as highlighted by its competitive link prediction performance, despite not being trained specifically for this task. Being the first approach to combine both of these desirable properties, NetGAN opens exciting avenues for further research.

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due to the non-unique, high-dimensional nature of graphs and the complex, non-local dependencies that exist between edges in a given graph.Here we propose GraphRNN, a deep autoregressive model that addresses the above challenges and approximates any distribution of graphs with minimal assumptions about their structure. GraphRNN learns to generate graphs by training on a representative set of graphs and decomposes the graph generation process into a sequence of node and edge formations, conditioned on the graph structure generated so far. In order to quantitatively evaluate the performance of GraphRNN, we introduce a benchmark suite of datasets, baselines and novel evaluation metrics based on Maximum Mean Discrepancy, which measure distances between sets of graphs.Our experiments show that GraphRNN significantly outperforms all baselines, learning to generate diverse graphs that match the structural characteristics of a target set, while also scaling to graphs 50 times larger than previous deep models.

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.