Loss or Gain: Hierarchical Conditional Information Bottleneck Approach for Incomplete Time Series Classification

Incomplete time series classification is both practically valuable and challenging as missing values in time series data are prevalent in real-world scenarios. Current approaches suffer from two major limitations. First, they overemphasize the consistency of data reconstruction during missing value imputation while neglecting the task-effectiveness of the imputed results for the classification. Second, they fail to systematically establish a synergistic optimization mechanism between data imputation and feature representation. To address these challenges, we propose a Hierarchical Conditional Information Bottleneck (HCIB) framework, which achieves incomplete time series classification through end-to-end joint optimization. Specifically, at the data imputation level, we re-examine the dual effects of missing data: the loss of critical information (Loss) versus the gain in interference suppression (Gain), elucidating this duality through bias-variance trade-off theory. Building on this analysis, we propose a task-information sufficiency criterion and extend the information bottleneck theory into a task-driven imputation framework by incorporating label information as a conditional constraint. At the feature representation level, we construct a hierarchical information bottleneck architecture to learn compressed yet informative temporal representations from the task-oriented imputed data. Furthermore, we derive the optimizable objective function for HCIB and design specialized neural network architectures for time series. Comprehensive experiments on multivariate and univariate time series datasets across multiple domains consistently demonstrate that the proposed method achieves significant improvements in classification performance compared to SOTA approaches.