Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and (2) graph neural networks (GNNs) based models that utilize the topological information from the inherent graph structure of MTS as relational inductive bias for imputation. Nevertheless, these methods either neglect topological information or assume the graph structure is fixed and accurately known. Thus, they fail to fully utilize the graph dynamics for precise imputation in more challenging MTS data such as networked time series (NTS), where the underlying graph is constantly changing and might have missing edges. In this paper, we propose a novel approach to overcome these limitations. First, we define the problem of imputation over NTS which contains missing values in both node time series features and graph structures. Then, we design a new model named PoGeVon which leverages variational autoencoder (VAE) to predict missing values over both node time series features and graph structures. In particular, we propose a new node position embedding based on random walk with restart (RWR) in the encoder with provable higher expressive power compared with message-passing based graph neural networks (GNNs). We further design a decoder with 3-stage predictions from the perspective of multi-task learning to impute missing values in both time series and graph structures reciprocally. Experiment results demonstrate the effectiveness of our model over baselines.

翻译：多变量时间序列（MTS）插值是近年来被广泛研究的问题。现有方法主要分为两类：（1）深度循环或生成模型，其专注于时间序列特征；（2）基于图神经网络（GNN）的方法，利用MTS固有图结构中的拓扑信息作为关系归纳偏置进行插值。然而，这些方法要么忽略拓扑信息，要么假设图结构固定且已知准确。因此，它们在更具挑战性的MTS数据（如网络化时间序列（NTS））中无法充分利用图动态特性以实现精准插值——此类数据的底层图结构会持续变化，且可能存在边缺失。本文提出一种新方法以克服上述局限。首先，我们定义了包含节点时间序列特征与图结构共同缺失的NTS插值问题。然后，设计了一种名为PoGeVon的新模型，利用变分自编码器（VAE）同时预测节点时间序列特征与图结构中的缺失值。特别地，我们在编码器中提出一种基于重启随机游走（RWR）的新型节点位置嵌入，其可证明比基于消息传递的图神经网络（GNN）具有更高的表达能力。此外，我们从多任务学习视角设计了一种包含三阶段预测的解码器，通过互惠方式插补时间序列与图结构中的缺失值。实验结果证明了本模型相对于基线方法的有效性。