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.
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