ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation

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.