Addressing Spatial-Temporal Heterogeneity: General Mixed Time Series Analysis via Latent Continuity Recovery and Alignment

Mixed time series (MiTS) comprising both continuous variables (CVs) and discrete variables (DVs) are frequently encountered yet under-explored in time series analysis. Essentially, CVs and DVs exhibit different temporal patterns and distribution types. Overlooking these heterogeneities would lead to insufficient and imbalanced representation learning, bringing biased results. This paper addresses the problem with two insights: 1) DVs may originate from intrinsic latent continuous variables (LCVs), which lose fine-grained information due to extrinsic discretization; 2) LCVs and CVs share similar temporal patterns and interact spatially. Considering these similarities and interactions, we propose a general MiTS analysis framework MiTSformer, which recovers LCVs behind DVs for sufficient and balanced spatial-temporal modeling by designing two essential inductive biases: 1) hierarchically aggregating multi-scale temporal context information to enrich the information granularity of DVs; 2) adaptively learning the aggregation processes via the adversarial guidance from CVs. Subsequently, MiTSformer captures complete spatial-temporal dependencies within and across LCVs and CVs via cascaded self- and cross-attention blocks. Empirically, MiTSformer achieves consistent SOTA on five mixed time series analysis tasks, including classification, extrinsic regression, anomaly detection, imputation, and long-term forecasting. The code is available at https://github.com/chunhuiz/MiTSformer.