Shapley-PC

This repository provides the code for the paper "Shapley-PC: Constraint-based Causal Structure Learning with Shapley Values". Shapley-PC is a constraint-based causal discovery algorithm, to faithfully recover the underlying causal graph from observational data.

There are four main python scripts:

• PC.py contains the pc() function that overrides the one from the causal-learn package to allow for our proposed decision rule. Example usage of this function is given below.
• spc.py contains the shapley_cs() functions that applies our proposed v-structure discovery algorithm within the pc() function.
• models.py contains the run_method() function that allows the run of our method as well as all the baselines used in the experiments.
• main.py reproduces the experiments. The parameters for the runs are loaded from the config folder (e.g. bnlearn_data). Example usage of this script is given below.

All the plots included in the paper can be inspected interactively from the results/figs folder. Just download them and open them in a browser.

A jupyter notebook collecting the stored results and producing the tables and plots in the paper is provided here.

Example usage

To run the Shapley-PC algorithm from python at the root folder, run:

# Imports
from PC import pc
from utils.helpers import random_stability
from utils.data_utils import load_bnlearn_data_dag
from utils.graph_utils import DAGMetrics

# Load alarm data
X_s, B_true = load_bnlearn_data_dag(dataset_name='alarm', data_path='datasets', sample_size=10000, seed=2024)

# Run SPC
random_stability(2024)
fitted = pc(data=X_s, alpha=0.01, show_progress=True, verbose=False)
B_est = fitted.G.graph.T

# Evaluate 
mt = DAGMetrics(B_est, B_true, sid=False)
metrics = ['nnz', 'shd', 'skF1', 'arrF1', 'immoral_UT_F1']
print({m:round(v,2) for m,v in mt.metrics.items() if m in metrics})

OUTPUT:
{'nnz': 55, 'arrF1': 0.52, 'skF1': 0.97, 'shd': 59.0, 'immoral_UT_F1': 0.69}

Reproduce Results

To reproduce the experiments, from a terminal at the root folder, run:

python main.py <synthetic_data,real_data,bespoke_config>

Beware, an end-to-end run of this script with the config provided takes several hours if run on single cpu since it contains all the scenarios. Modify it to run only part of it in one go.

Datasets

The datasets used for the synthetic data are created within the main.py function. Some of the bnlearn datasets are provided in .rds since no .bif are available in the bnlearn repository for the gaussian and conditional linear gaussian Bayesian Networks. The data was generated in a R environment, for 10 seeds, using the script provided here. .pkl files that are picked up by the main.py function to reproduce the experiments are provided for these data, these were produced using this script.

Requirements

The code was tested with Python 3.10.12. requirements.txt provides the necessary python packages. Run pip install -r requirements.txt from a terminal at the root folder to install all packages in your virtual environment.

Note that the R dependencies for CausalDiscoveyToolbox need separate installation. install_script.R installs the necessary R packages but this needs to be ran from R while in the root folder. R-4.1.2 was used for the testing.

Reference

If you are using this code, please cite our paper

@InProceedings{pmlr-v275-russo25a,
  title = 	 {Shapley-PC: Constraint-based Causal Structure Learning with a Shapley Inspired Framework},
  author =       {Russo, Fabrizio and Toni, Francesca},
  booktitle = 	 {Proceedings of the Fourth Conference on Causal Learning and Reasoning},
  pages = 	 {292--339},
  year = 	 {2025},
  editor = 	 {Huang, Biwei and Drton, Mathias},
  volume = 	 {275},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {07--09 May},
  publisher =    {PMLR},
  pdf = 	 {https://raw.githubusercontent.com/mlresearch/v275/main/assets/russo25a/russo25a.pdf},
  url = 	 {https://proceedings.mlr.press/v275/russo25a.html}
}