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This is the official code for our accepted ICML 2026 paper: Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series.

SCALE (Spectral Conformal prediction via wAveLEt transform) studies conformal prediction under non-exchangeability in graph-structured multivariate time series.

SCALE is a two-stage project for uncertainty-aware spatiotemporal forecasting:

• Stage 1: Train a base forecasting model (RNN / STGNN / Transformer / DCRNN / GraphWaveNet / AGCRN / VAR, etc.) and save residuals plus indices.
• Stage 2: Use the SCALE quantile model to apply spectral graph wavelet (SGWT) low/high-frequency decoupling, combining a low-frequency non-exchangeable backbone, high-frequency exchangeable statistics, and gating to output multi-quantile prediction intervals.

The project uses PyTorch Lightning and Torch Spatiotemporal (tsl) for training and data pipelines. All outputs are written to logs/.

• basicts/: shared components (predictors, metrics, residual utilities, logging).
• conformal_model/scale/: SCALE model implementation and configs (SGWT, decoupled components, backbones, losses).
• foundation_model/: base-model training configs (Hydra-style YAML).
• experiments/: experiment entry points (base training, SCALE training, config runner).
• datasets/: datasets directory (includes MetrLA, PeM昭和04年07月08日 samples).
• logs/: training logs and artifacts.
• config.yaml: global path configuration (data, logs, etc.).
• install.txt: dependency install hints.

Core deps (from imports in code):

• PyTorch + PyTorch Lightning
• torch-geometric and its extensions (pyg_lib, torch_scatter, torch_sparse, torch_cluster, torch_spline_conv)
• torch-spatiotemporal (tsl)
• omegaconf, hydra-core
• tensorboard / tensorboardX

Install from install.txt (make sure CUDA matches your local PyTorch build):

pip install torch_geometric
pip install pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv -f https://data.pyg.org/whl/torch-2.8.0+cu129.html
pip install torch-spatiotemporal
pip install omegaconf
pip install hydra-core
pip install tensorboard
pip install tensorboardX

Default entry point:

python experiments/run_base_model.py

This reads configs from foundation_model/training/ (default default.yaml) and saves residuals:

• logs/base/<dataset>/<model>/<date>/<time>/residuals.h5
• logs/base/<dataset>/<model>/<date>/<time>/indices.npz
• logs/base/<dataset>/<model>/<date>/<time>/config.yaml

To change model/dataset, edit YAML files under foundation_model/training/ (e.g., dataset/*.yaml, model/*.yaml).

SCALE configs are Python files with a CONFIG dict. Use the config runner:

1. Open conformal_model/scale/config/<dataset>.py and set src_dir to the Stage-1 output directory.
2. Run:

python experiments/run_config.py --config conformal_model/scale/config/la.py

Outputs go to:

• logs/scale/<dataset>/scale/<date>/<time>/

This folder includes metrics.json, runner.log, Lightning checkpoints, and TensorBoard logs.

Entry: foundation_model/training/default.yaml

• dataset: dataset name and split strategy (splitting)
• model: model configuration (RNN/STGNN/Transformer/DCRNN/GWNet/AGCRN, etc.)
• optimizer / lr / weight_decay: optimizer setup
• window / horizon / stride / delay: temporal windowing
• apply_scaler / scale_axis: normalization settings

Entry: conformal_model/scale/config/*.py Key fields:

• src_dir: Stage-1 output directory (required)
• alphas: target miscoverage, e.g. [0.05, 0.1, 0.2]
• window / horizon: must match Stage-1 (strict check)
• val_len: validation split ratio for calibration data
• apply_scaler / scale_axis: normalization settings
• dataset.connectivity: graph construction
• model.hparams.model: SGWT and backbone params (n_scales, kernel_type, n_high_scales, enable_gating, etc.)

Supported datasets (see experiments/run_base_model.py and experiments/run_scale.py):

• la (MetrLA)
• pems03, pems04, pems07, pems08
• pems_bay
• large_st

Data is expected under datasets/. If you use a tsl dataset that is not present locally, the first run may trigger a download.

SCALE computes and logs multi-quantile metrics:

• Pinball Loss
• Coverage / Delta Coverage
• Prediction Interval Width (PIW)
• Winkler Score

Results are saved in metrics.json, with per-alpha summaries under metrics.per_alpha.

• src_dir is empty: ensure SCALE config points to a directory containing residuals.h5, indices.npz, and config.yaml.
• horizon mismatch: Stage-2 enforces the same horizon as Stage-1.
• GPU/CPU: scripts auto-select GPU if available, otherwise CPU; CPU training is slower.

• Base model training: experiments/run_base_model.py
• SCALE training: experiments/run_scale.py
• Python config runner: experiments/run_config.py

For adding new models, changing backbones, or modifying SGWT details, start with:

• conformal_model/scale/arch/spec_decoupled_components.py
• conformal_model/scale/arch/backbones/
• conformal_model/scale/arch/spectral/

We sincerely appreciate the great contribution of the following works:

• CoREL

@article{guo2026delving,
 title={Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series},
 author={Guo, Ruichao and Han, Xingyao and Luo, Wenshui and Liu, Zhe and Gong, Chen and Wang, Hesheng},
 journal={arXiv preprint arXiv:2605.04957},
 year={2026}
}