GraphMDN: Leveraging graph structure and deep learning to solve inverse problems

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