## 7 Conclusions  
CoTD-VAE effectively improves the model's performance on reconstruction and classification tasks by disentangling time series data into latent factors such as static features,long-term trends, and abrupt events, and by introducing temporal consistency constraints such as trend smoothness and event sparsity. The CoTD-VAE's disentanglement mechanism enables the model to extract different types of information from the time series. This meaningful decomposition enhances the model's interpretability, allowing us to gain insight into the contribution of different latent factors to classification and providing more valuable features for downstream tasks. This is expected to significantly improve the accuracy and clinical utility of classification in medical time series data. Future work can explore the following directions:  
* Further optimization of model architecture: Exploring more advanced sequence modeling architectures (e.g., more complex attention mechanisms) or different disentanglement methods to further enhance the separability and expressiveness of latent representations. Also, investigating how to adaptively determine the dimensions of each latent space and the weights of the regularization terms (e.g., the \(\beta\) and \(\lambda\) parameters) instead of using fixed hyperparameter settings. * More fine-grained latent factor analysis and clinical association: Conducting more in-depth analysis of the disentangled static, trend, and event latent spaces, for example, by using clustering, visualization, or other statistical methods, to identify clinically meaningful subgroups or patterns. Crucially, future work will involve close collaboration with clinical experts to validate the specific interpretations of these learned latent factors and to assess their association strength with specific disease states or risk events. * Application to wider medical time series tasks: Applying the CoTD-VAE model to other types of medical time series data (e.g., physiological waveforms, continuous glucose monitoring data, etc. ), as well as different clinical tasks, such as early disease diagnosis, disease progression prediction, treatment response assessment, or patient phenotyping. * Enhancing model generalization ability and transferability: Investigating how to improve the generalization ability of trained models across different hospitals or patient populations. Exploring federated learning or transfer learning techniques in order to utilize data from multiple sources while protecting data privacy, aiming to train more robust models. * Integration with causal inference: Exploring the combination of disentangled representations with causal inference methods to better understand the causal relationships between different latent factors and how they jointly influence patient risk outcomes. This will help reveal the underlying disease mechanisms and provide guidance for clinical interventions. These future research directions will further advance the development of medical time series analysis and risk prediction techniques based on deep generative models and disentangled representation learning. Conceptualization, L.H. ; methodology, L.H. and Q.C. ; software, L.H. ; validation, L.H. ; formal analysis, L.H. ; investigation, L.H. ; resources, Q.C. ; data curation, L.H. ; writing--original draft preparation, L.H. ; writing--review and editing, Q.C. ; visualization, L.H. ; supervision, Q.C. ; project administration, Q.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the Specific Research Project of Guangxi for Research Bases and Talents (GuiKe AD24010011) and the Key Research & Development Program Project of Guangxi (GuiKe AB25069095). **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The MIMIC-IV dataset can be accessed via the PhysioNet platform, and the UCI HAR dataset is available from the UCI Machine Learning Repository.