Bootstrap aggregation and confidence measures to improve time series causal discovery

In this folder, you can find the official implementation of the numerical experiments of the paper:

Debeire, K., Runge, J., Gerhardus, A., Eyring, V. (2024). Bootstrap aggregation and confidence measures to improve time series causal discovery (see arXiv article). Accepted at the 3rd Conference on Causal Learning and Reasoning (CLeaR 2024).

A method to perform bootstrap aggregation of time series causal graphs and measure a confidence for links of the aggregated graph. Here combined with the PCMCI+ algorithm from the TIGRAMITE package. We provide here the code that can be used to recreate figures 3, 4, and 5 as presented in the paper.

Author: Kevin Debeire, kevin.debeire@dlr.de

The current release on Zenodo can be found here:

Requirements

First setup a conda environment (by default called bagged_pcmci) from the environment.yml file:

conda env create -f environment.yml

Activate this environment.

As explained in the paper, our bagging approach and confidence measures is combined with the PCMCI+ causal discovery algorithm. The PCMCI+ method is implemented in the TIGRAMITE package. Follow the instructions below to install TIGRAMITE.

First clone the TIGRAMITE repository:

git clone https://github.com/jakobrunge/tigramite.git

and point to this specific commit

git reset --hard 27ded041e87f8d9a8d5f8714e8db5c1235e8616a

Then, our bagging and confidence measures method is implemented in the scripts provided in the folder to_replace_in_tigramite/.

You will have to replace the TIGRAMITE pcmci_base.py and data_processing.py files in tigramite/tigramite with the ones provided in to_replace_in_tigramite/, respectively pcmci_base.py and data_processing.py.

The modified pcmci_base.py and data_processing.py include the bagging and confidence measures introduced in the paper.

Then install TIGRAMITE:

python setup.py install

You should now be able to run the numerical experiments and reproduce the figures of the paper.

Generating numerical experiments data and plotting figures

Find below the instructions to produce the figures 2, 3, 4A, 4B of the main text and 5 to 17 of the appendix. All model and method parameters of the scripts may need to be adjusted to reproduce the figures.

Please also adjust the save paths (by default ./ ) in the scripts. They specify where the numerical results are saved, and where the figures are saved.

Generation of the synthetic data:

If you have access to an HPC system with a slurm job scheduler:

• fill in the sbatch_XXX.sh scripts. Specify your account, partition, number of cores per CPU, etc...
• adjust the model parameters and methods in the create_submission_figXXX.py scripts to reproduce a given figure.
• run: 'python create_submission_figXXX.py 1'. This will submit a job for each configuration (for example each alpha_pc of PCMCI+, number of variables, sample size, etc...) in which the Bagged-PCMCI+ and PCMCI+ (or PC/LPCMCI) are evaluated on the generated synthetic data.

Alternatively, it can be run locally, but this is not recommended as the computational cost to run the numerical experiments are high:

• set run_locally=True and submit=False in create_submission_figXXX.py
• adjust the model parameters and methods in the create_submission_figXXX.py scripts to reproduce a given figure.
• run: 'python create_submission_figXXX.py 1'

For fig4A, check the model parameters in compute_fig4A.py and run: 'python compute_fig5A.py'. For fig4B, once all computations are done, run: 'python compute_metrics_fig5B.py'. This will calculate the mean absolute frequencies errors.

Plotting:

Once the data has been generated, you can plot the figures:

• Use the plotting script matching the figure you want to reproduce.
• You may need to adjust the values of the model parameters and methods in the plotting scripts.
• For figure 4A, simply run 'python plot_fig4A.py' to reproduce the figure 4A.
• For the other figures, the script expects arguments which describes the type of experiments. For example, run 'python plot_figXXX.py par_corr pc_alpha_highdegree'. The first argument indicates the Conditional Independence test: par_corr (all linear experiments) or gp_dc (nonlinear experiment). The second arguments includes the name of the varying parameters (pc_alpha,sample_size,highdim,tau_max,autocorr) and additional arguments like the degree of cross-links ("highdegree"), the noise distribution ("mixed"), nonlinearity ("nonlinear"), or "boot_rea" for figure 4B. We give a list of the arguments for each figure below.

List of command to run to plot a figure:

• fig2/5 (like fig6/7 and 8/9 and 10/11): 'python plot_fig2and5to17.py par_corr pc_alpha_highdegree' (only the values of the model parameters change)
• fig3a: 'python plot_fig3.py par_corr highdim_highdegree'
• fig3b: 'python plot_fig3.py par_corr sample_size_highdegree'
• fig3c: 'python plot_fig3.py par_corr autocorr_highdegree'
• fig3d: 'python plot_fig3.py par_corr tau_max_highdegree'
• fig4a: 'python plot_fig4A.py'
• fig4b: 'python plot_fig4B.py par_corr boot_rea_highdegree'
• fig12a: 'python plot_fig2and5to17.py par_corr pc_alpha_highdegree_mixed'
• fig12b: 'python plot_fig2and5to17.py par_corr pc_alpha_highdegree_nonlinear'
• fig14/15: 'python plot_fig2and5to17.py par_corr pc_alpha_highdegree' (make sure to change the methods)
• fig16/17: 'python plot_fig2and5to17.py par_corr pc_alpha_highdegree' (make sure to change the methods)

License

GNU General Public License v3.0

See license.txt for full text.