  We consider the problem of modelling high-dimensional distributions and
generating new examples of data with complex relational feature structure
coherent with a graph skeleton. The model we propose tackles the problem of
generating the data features constrained by the specific graph structure of
each data point by splitting the task into two phases. In the first it models
the distribution of features associated with the nodes of the given graph, in
the second it complements the edge features conditionally on the node features.
We follow the strategy of implicit distribution modelling via generative
adversarial network (GAN) combined with permutation equivariant message passing
architecture operating over the sets of nodes and edges. This enables
generating the feature vectors of all the graph objects in one go (in 2 phases)
as opposed to a much slower one-by-one generations of sequential models,
prevents the need for expensive graph matching procedures usually needed for
likelihood-based generative models, and uses efficiently the network capacity
by being insensitive to the particular node ordering in the graph
representation. To the best of our knowledge, this is the first method that
models the feature distribution along the graph skeleton allowing for
generations of annotated graphs with user specified structures. Our experiments
demonstrate the ability of our model to learn complex structured distributions
through quantitative evaluation over three annotated graph datasets.
