AZ-whiteness test

This repository is the official implementation of AZ-whiteness test of our paper:

Daniele Zambon, Cesare Alippi. AZ-whiteness test: a test for signal uncorrelation on spatio-temporal graphs. 2022.

@inproceedings{zambon2022aztest,
 author = {Zambon, Daniele and Alippi, Cesare},
 booktitle = {Advances in Neural Information Processing Systems},
 title={AZ-whiteness test: a test for signal uncorrelation on spatio-temporal graphs},
 year = {2022},
 url={https://arxiv.org/abs/2204.11135},
}

Requirements

Experiments are run with Python3.8. All requirements should be specified in file aztest-w-tsl.yml. A working conda enviroment can be created by running

conda env create --file=aztest-w-tsl.yml

Datasets MetrLA and PemsBay are automatically retrieved from TorchSpatiotemporal library, whereas GPVAR data can be downloaded from the following link https://drive.switch.ch/index.php/s/qKaRyjJ0kSlnZN1 and should be placed in folder data/gpvar-T30000_line-c5.

Structure of the repository

The structure of the repository is the following:

• graph_sign_test.py implements the AZ-test and some utilities to analyze the prediction residuals.
• triangular_tricom_graph.py implements a family of graphs, and exposes plotting utilities.
• synthetic_residuals.py implements several targeted synthetic tests on correlated graph signals.
• graph_polynomial_var.py implements the GPVAR model and provides a dataset class usable in TorchSpatiotemporal and torch nn model.
• tsl_experiments.py extends the traffic forecasting example in TorchSpatiotemporal adding GPVAR model and data.

Figures generated by script synthetic_residuals.py are stored in folder results, and results of tsl_experiments.py are stored in folder log.

Configuration files with model and training hyperparameters are in located in folder config/traffic.

Experiments and figures of the paper

The experiments of the arXiv version of the paper are run with the following commands.

• Figure 3 is generated by calling main("power-unimodal", disable_warning=True) and main("power-mixture", disable_warning=True) in synthetic_residual.py.
• Table 2 (as well as its extension, Table 3 in supplementary material) is obtained from bash script run_all_experiments.sh that calls tsl_experiments.py; a summary table with all results is obtained by running fetch_results.sh after having listed the desired checkpoints from ./log into it.
• Figure 4 and Figure 6 (supplementary material) are generated during the runs of tsl_experiments.py with --dataset-name gpolyvar and stored in folder data/gpvar-T30000_line-c5.
• Figure 5 (supplementary material) is generated by calling main("viz") in synthetic_residual.py.
• Figure 7 (supplementary material) is generated by calling main("sparse-full") in synthetic_residual.py.