Time-series domain adaptation via sparse associative structure alignment: Learning invariance and variance

Domain adaptation on time-series data, which is often encountered in the field of industry, like anomaly detection and sensor data forecasting, but received limited attention in academia, is an important but challenging task in real-world scenarios. Most of the existing methods for time-series data use the covariate shift assumption for non-time-series data to extract the domain-invariant representation, but this assumption is hard to meet in practice due to the complex dependence among variables and a small change of the time lags may lead to a huge change of future values. To address this challenge, we leverage the stableness of causal structures among different domains. To further avoid the strong assumptions in causal discovery like linear non-Gaussian assumption, we relax it to mine the stable sparse associative structures instead of discovering the causal structures directly. Besides the domain-invariant structures, we also find that some domain-specific information like the strengths of the structures is important for prediction. Based on the aforementioned intuition, we extend the sparse associative structure alignment model in the conference version to the S parse A ssociative S tructure A lignment model with domain-specific information enhancement ( SASA2 in short), which aligns the invariant unweighted spare associative structures and considers the variant information for time- series unsupervised domain adaptation. Specifically, we first generate the segment set to exclude the obstacle of offsets. Second, we extract the unweighted sparse associative structures via sparse attention mechanisms. Third, we extract the domain-specific information via an autoregressive module. Finally, we employ a unidirectional alignment restriction to guide the transformation from the source to the target. Moreover, we further provide a generalization analysis to show the theoretical superiority of our method. Compared with existing methods, our method yields state-of-the-art performance, with a 5% relative improvement in three real-world datasets, covering different applications: air quality, in-hospital healthcare, and anomaly detection. Furthermore, visualization results of sparse associative structures illustrate what knowledge can be transferred, boosting the transparency and interpretability of our method.