  The recent introduction of Graph Neural Networks (GNNs) and their growing
popularity in the past few years has enabled the application of deep learning
algorithms to non-Euclidean, graph-structured data. GNNs have achieved
state-of-the-art results across an impressive array of graph-based machine
learning problems. Nevertheless, despite their rapid pace of development, much
of the work on GNNs has focused on graph classification and embedding
techniques, largely ignoring regression tasks over graph data. In this paper,
we develop a Graph Mixture Density Network (GraphMDN), which combines graph
neural networks with mixture density network (MDN) outputs. By combining these
techniques, GraphMDNs have the advantage of naturally being able to incorporate
graph structured information into a neural architecture, as well as the ability
to model multi-modal regression targets. As such, GraphMDNs are designed to
excel on regression tasks wherein the data are graph structured, and target
statistics are better represented by mixtures of densities rather than singular
values (so-called ``inverse problems"). To demonstrate this, we extend an
existing GNN architecture known as Semantic GCN (SemGCN) to a GraphMDN
structure, and show results from the Human3.6M pose estimation task. The
extended model consistently outperforms both GCN and MDN architectures on their
own, with a comparable number of parameters.
