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Aligning Time-series by Local Trends: Applications in Public Health
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Proposes DTW+SBA, an ensemble method that aligns epidemic trajectories by local trends using shapelet-space representations combined with DTW barycenter averaging, preserving peak timing and size better than mean ensembles.
Problem
Mean and median ensembles of epidemic projections from multiple models aggregate only along the scale axis at each time point, which misrepresents underlying trajectories (e.g., underestimates peaks), hindering public health communication and policy.
Approach
Combine a closeness-preserving shapelet-space representation of local trends (with proofs on the minimal number of shapelets, w−1 plus a flat shapelet) with DTW barycenter averaging, so that trajectories are aligned by ordered local trends and the ensemble is averaged over both timing and scale.
Key results
- DTW+SBA is the only ensemble method that captures peak timing and size of underlying trajectories well across all 12 datasets (Table 1), while the mean ensemble underrepresents peaks.
- The paper proves w−1 linearly independent shapelets plus a flat shapelet are necessary and sufficient for closeness-preserving shapelet-space representation.
- DTW+S clustering of 75 influenza hospitalization trajectories yields four clusters of similarly shaped curves, whereas normalized DTW and shapelet-only measures mix distinct patterns.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DTW+S barycenter averaging instead of mean ensembling | epidemic trajectory ensembles · Sets 1–12 | peak size and timing fractional error: Set 7 peak size: -0.37 -> -0.03; peak timing: -0.10 -> 0.07 | Helped |
| Use DTW+S barycenter averaging instead of DTW barycenter averaging | epidemic trajectory ensembles · Sets 1–12 | peak size and timing fractional error: Set 7 peak size: -0.37 -> -0.03; peak timing: -0.10 -> 0.07 | Helped |
| Use DTW+S alignment rather than normalized DTW for clustering | influenza hospitalization trajectories · Set 1 clustering | cluster quality | Helped |
| Use DTW+S alignment rather than shapelet-only distance for clustering | influenza hospitalization trajectories · Set 1 clustering | cluster quality | Helped |
Surprising findings
- Standard DTW barycenter averaging with z-normalization produces nearly identical results to the mean ensemble and flattens peaks.
Limitations
- Choosing appropriate shapelets requires domain knowledge when extending to other fields.
- Current implementation has O(dwT) time and space cost; optimizations of DTW not yet explored.
- Evaluation is on scenario projections without ground truth, relying on proxy statistics of peak timing and size.
Experimental setup
Datasets: Influenza Scenario Modeling Hub Round 4 trajectories RSV Scenario Modeling Hub Round 1 trajectories single influenza hospitalization model trajectories (75)
Benchmarks: Influenza Scenario Modeling Hub Round 4 RSV Scenario Modeling Hub Round 1
Metrics: fractional error in peak size fractional error in peak timing silhouette coefficient (clustering)
Baselines: mean ensemble DTW BA DTW (z-norm) BA Euclidean distance (normalized) shapelet-only distance
Builds on: Dynamic Time Warping DTW barycenter averaging shapelet-space representation
Closest papers by meaning
- SPATIALEPIBENCH: Benchmarking Spatial Information and Epidemic Priors in Forecasting (NeurIPS 2026 · similarity 0.86)
- Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis (NeurIPS 2024 · similarity 0.81)
- An Empirical Examination of Balancing Strategy for Counterfactual Estimation on Time Series (ICML 2024 · similarity 0.81)
- EARTH: Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph (ICML 2025 · similarity 0.81)
- MOMENT: A Family of Open Time-series Foundation Models (ICML 2024 · similarity 0.80)
- Discovering Latent Causal Graphs from Spatiotemporal Data (ICML 2025 · similarity 0.80)
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