Missing data is a pervasive issue in both scientific and engineering tasks, especially for the modeling of spatiotemporal data. This problem attracts many studies to contribute to machine learning solutions. Existing imputation solutions mainly include low-rank models and deep learning models. On the one hand, low-rank models assume general structural priors, but have limited model capacity. On the other hand, deep learning models possess salient features of expressivity, while lack prior knowledge of the spatiotemporal process. Leveraging the strengths of both two paradigms, we demonstrate a low rankness-induced Transformer model to achieve a balance between strong inductive bias and high model expressivity. The exploitation of the inherent structures of spatiotemporal data enables our model to learn balanced signal-noise representations, making it versatile for a variety of imputation problems. We demonstrate its superiority in terms of accuracy, efficiency, and generality in heterogeneous datasets, including traffic speed, traffic volume, solar energy, smart metering, and air quality. Comprehensive case studies are performed to further strengthen interpretability. Promising empirical results provide strong conviction that incorporating time series primitives, such as low-rank properties, can substantially facilitate the development of a generalizable model to approach a wide range of spatiotemporal imputation problems.

翻译：数据缺失是科学和工程任务中的普遍问题，尤其是在时空数据建模中。这一问题吸引了众多研究致力于机器学习解决方案。现有的插补方法主要包括低秩模型和深度学习模型。一方面，低秩模型假设通用结构先验，但模型容量有限；另一方面，深度学习模型具备显著的表达能力，却缺乏时空过程的先验知识。结合两种范式的优势，我们提出了一种低秩性诱导的Transformer模型，以在强归纳偏差与高模型表达能力之间取得平衡。对时空数据内在结构的利用使我们的模型能够学习均衡的信号-噪声表示，从而适用于多种插补问题。我们展示了其在异质数据集（包括交通速度、交通流量、太阳能、智能计量和空气质量）中在准确性、效率和通用性方面的优越性。通过全面的案例研究进一步增强了模型的可解释性。令人鼓舞的实验结果有力地表明，融入时间序列基元（如低秩性质）可显著促进开发通用模型，以处理广泛的时空插补问题。