Disentangling Dynamics: Advanced, Scalable and Explainable Imputation for Multivariate Time Series

Missing values pose a formidable obstacle in multivariate time series analysis. Existing imputation methods rely on entangled representations that struggle to simultaneously capture multiple orthogonal time-series patterns, leading to suboptimal performance and limited interpretability. Meanwhile, requiring the entire data span as input renders these models impractical for long time series. To address these issues, we propose <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf TIDER}$</tex-math></inline-formula> and its enhanced version, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf AdaTIDER}$</tex-math></inline-formula>. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf TIDER}$</tex-math></inline-formula> employs low-rank matrix factorization and disentangled temporal representations to model intricate dynamics like trend, seasonality, and local bias. However, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf TIDER}$</tex-math></inline-formula> is limited to single-period modeling and does not explicitly capture dependencies between channels. To overcome these limitations, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf AdaTIDER}$</tex-math></inline-formula> incorporates adaptive cross-channel dependency modeling and multi-period seasonality representations. These advancements enable it to dynamically capture variable relationships and complex multi-period patterns, significantly enhancing imputation accuracy and interpretability, while maintaining <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math>${\sf TIDER}$</tex-math></inline-formula>'s scalability. Extensive experiments on real-world datasets validate the superiority of our models in imputation accuracy, scalability, interpretability, and robustness.