Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical variational Bayes to implicitly capture posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and highly correlated latent structures. We show that the existing semi-implicit variational inference objective provably reduces information in the observed graph. Based on this observation, we estimate and add an additional mutual information term to the semi-implicit variational inference learning objective to capture rich correlations arising between the input and latent spaces. We show that the inclusion of this regularization term in conjunction with the Poincare embedding boosts the quality of learned high-level representations and enables more flexible and faithful graphical modeling. We experimentally demonstrate that our approach outperforms existing graph variational auto-encoders both in Euclidean and in hyperbolic spaces for edge link prediction and node classification.
翻译:对物理、社会和信息科学中产生的关系数据进行高效建模具有挑战性,因为数据内部依赖性复杂。在这项工作中,我们从半隐含图形变异自动编码器中建立半隐含图形自动编码器,以以低维图形潜在代表形式获取更高层次的统计数据。我们通过一个 Poincare 嵌入以高效代表显示等级结构的图表,将双曲几何方法纳入潜藏空间。为了处理传统变异推断中天真的后视潜在分布假设,我们使用半隐含等级变异贝来隐含地捕捉特定图形数据的后端,这些数据可能显示重尾部、多种模式、偏差和高度关联的潜伏结构。我们显示,现有的半隐含不显性变异图目标会减少观测图中的信息。基于这一观察,我们估计并增加一个半隐含隐含的变异种学习目标,以捕捉到输入空间和潜在空间之间产生的丰富关联。我们显示,将这一整形术语与Poincare 嵌入模型、多种模式、隐蔽度和高度隐含的潜伏结构,从而展示了我们所学的图像水平的高级图变变的图像,从而得以更灵活地显示了我们目前的图变的图像的图像和变形图。