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Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling
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Proposes Hierarchical Downsampling Spatiotemporal Time Series (HDTTS-style) model that coarsens inputs over time and space, combining multi-scale representations with an interpretable attention decoder to forecast graph time series under missing data.
Problem
Spatiotemporal forecasting on sensor graphs when input observations are missing, especially in contiguous spatiotemporal blocks, where standard STGNNs assume complete inputs and fail to capture dynamics.
Approach
Hierarchical time-then-space downsampling: temporal layers decimate sequences by a factor d while k-MIS graph pooling coarsens the graph, producing a pool of multi-scale representations that are weighted per node by a soft attention conditioned on observations and the missing-data mask, with no imputation step.
Key results
- On MSO with block-propagated missing data, the IMP variant reaches MAE 0.651 versus 0.669 for TTS-AMP, the strongest baseline.
- On ENGRAD (block-prop missing), MODEL-IMP reaches MAE 4.64 versus 4.81 for TTS-IMP and 4.70 (block) vs 4.48 for MODEL-IMP.
- On PVUS, MODEL-IMP trains at 7.11 batches/s with 10.86 GB GPU RAM, faster than TTS-AMP (14.26 batches/s is faster, so comparison is mixed) and far more efficient than DCRNN and AGCRN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-IMP versus TTSAMP · MSODS block_prop | MAE: 0.669 ±0.013 -> 0.651 ±0.023 | Helped |
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-IMP versus TTSAMP · EngRAD block_prop | MAE: 4.81 ±0.06 -> 4.64 ±0.03 | Helped |
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-AMP versus TTSAMP · AIR + Point | MAE: 16.15 ±0.05 -> 15.76 ±0.07 | Helped |
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-IMP versus TTSAMP · PVUS block | MAE: 3.46 ±0.03 -> 3.47 ±0.01 | No clear effect |
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-AMP versus TTSAMP · PVUS block_prop | MAE: 3.65 ±0.05 -> 3.61 ±0.02 | Helped |
| Use hierarchical spatiotemporal downsampling with adaptive scale attention | Model-IMP versus TTSAMP · MSODS point (5%) | MAE: 0.063 ±0.003 -> 0.058 ±0.004 | Helped |
Surprising findings
- Non-trainable pooling can limit performance when the input graph is noisy or does not reflect the actual correlations (traffic experiment in appendix).
- Forecasting-specific baselines with imputation (GRIN) perform strongly on point missing but degrade more than the proposed method under block-propagated missingness.
Limitations
- Relies on non-trainable k-MIS pooling that depends strongly on graph topology, which may be too restrictive for noisy graphs.
- Evaluated only on a limited set of datasets with simulated missing patterns for most settings.
Experimental setup
Datasets: MSO AIR ENGRAD PVUS
Benchmarks: MSO AIR ENGRAD PVUS
Metrics: MAE batches per second GPU RAM
Baselines: DCRNN GraphWaveNet AGCRN TTS-IMP TTS-AMP TAS-IMP TAS-AMP GRU-D GRU-I GRIN GRU
Builds on: GRU diffusion convolution k-MIS pooling GRIN Select-Reduce-Connect
Closest papers by meaning
- Taming Local Effects in Graph-based Spatiotemporal Forecasting (NeurIPS 2023 · similarity 0.92)
- Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting (ICLR 2025 · similarity 0.89)
- ST-FiT: Inductive Spatial-Temporal Forecasting with Limited Training Data (AAAI 2025 · similarity 0.88)
- Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data (AAAI 2024 · similarity 0.87)
- How Different from the Past? Spatio-Temporal Time Series Forecasting with Self-Supervised Deviation Learning (NeurIPS 2025 · similarity 0.87)
- Towards Dynamic Spatial-Temporal Graph Learning: A Decoupled Perspective (AAAI 2024 · similarity 0.86)
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