Missing Value Imputation in Relational Data Using Variational Inference

In real-world networks, node attributes are often only partially observed, necessitating imputation to support analysis or enable downstream tasks. However, most existing imputation methods overlook the rich information contained within the connectivity among nodes. This research is inspired by the premise that leveraging all available information should yield improved imputation, provided a sufficient association between attributes and edges. Consequently, we introduce a joint latent space model that produces a low-dimensional representation of the data and simultaneously captures the edge and node attribute information. This model relies on the pooling of information induced by shared latent variables, thus improving the prediction of node attributes and providing a more effective attribute imputation method. Our approach uses variational inference to approximate posterior distributions for these latent variables, resulting in predictive distributions for missing values. Through numerical experiments, conducted on both simulated data and real-world networks, we demonstrate that our proposed method successfully harnesses the joint structure information and significantly improves the imputation of missing attributes, specifically when the observed information is weak. Additional results, implementation details, a Python implementation, and the code reproducing the results are available online. Supplementary materials for this article are available online.在现实世界的网络中，节点属性通常仅能被部分观测到，因此需要通过属性插补来支撑后续分析或下游任务。然而，绝大多数现有插补方法均忽略了节点间连接关系所蕴含的丰富信息。本研究的灵感源自如下前提：只要节点属性与边之间存在足够强的关联，充分利用所有可用信息即可实现更优的属性插补效果。据此，我们提出了一种联合隐空间模型，该模型可生成数据的低维表征，同时捕获边与节点属性两类信息。该模型依托共享隐变量所诱导的信息聚合机制，能够提升节点属性的预测精度，进而提供一种更为高效的属性插补方案。我们的方法采用变分推断来近似这些隐变量的后验分布，从而得到缺失值的预测分布。通过在模拟数据与现实网络数据集上开展数值实验，我们证明所提方法能够有效利用联合结构信息，在观测信息较为匮乏的场景下，显著提升缺失属性的插补效果。本文的补充结果、实现细节、Python实现代码以及复现实验结果的代码均可在线获取，本文的补充材料同样可在线查阅。