We introduce the Graph Mixture Density Networks, a new family of machine
learning models that can fit multimodal output distributions conditioned on
graphs of arbitrary topology. By combining ideas from mixture models and graph
representation learning, we address a broader class of challenging conditional
density estimation problems that rely on structured data. In this respect, we
evaluate our method on a new benchmark application that leverages random graphs
for stochastic epidemic simulations. We show a significant improvement in the
likelihood of epidemic outcomes when taking into account both multimodality and
structure. The empirical analysis is complemented by two real-world regression
tasks showing the effectiveness of our approach in modeling the output
prediction uncertainty. Graph Mixture Density Networks open appealing research
opportunities in the study of structure-dependent phenomena that exhibit
non-trivial conditional output distributions.

该研究提出了一种新的机器学习模型 —— 图混合密度网络，可适用于任意拓扑结构的多模态输出分布拟合。研究结果表明，该模型在应对结构化数据相关的挑战性条件密度估计问题方面表现突出，并可应用于随机传染病模拟等领域，且能有效提高结果的预测不确定性。

图混合密度网络

Graph Mixture Density Networks

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.

本文研究了新型的图神经网络 (Graph Neural Networks) 在处理非欧几里德图结构数据时的应用。作者提出了一种将 Graph Neural Network 和混合密度网络 (Mixture Density Network, MDN) 相结合的新型网络 (Graph Mixture Density Network), 该网络可将图结构信息嵌入到深度神经网络中，并在数据具有图结构、有多模态回归目标或是需要模拟多峰分布的情况下表现优异。作者在基于人类姿势估计的任务中，比较了该网络与其他现有的图神经网络模型，结果表明该模型有效地提升了预测性能。