🌈 BNN-CC

This is the implementation of the paper "Causal structure-enhanced branch neural networks for interpretable and robust regression", published at Expert Systems With Applications (Elsevier ESWA) in 2026.

📋 Overview

In this paper, we propose a novel framework called BNN-CC. The figure below illustrates the overall framework of our BNN-CC.

📁 Project Directory Structure

BNNCC-codes/
├── README.md
├── requirements.txt
├── LICENSE.txt
├── main_IHDP.py
├── utils.py
├── causal_discovery.py
├── data_loader.py
├── models/
│   └── bnncc_regression.py
└── data/
    ├── ihdp/
    │   ├── variables_description_IHDP_EN.csv
    │   ├── train_df.csv
    │   └── test_df.csv
    └── twins/
        ├── variables_description_twins_EN.csv
        └── data_twins.csv

🚀 How To Run

• Installation: environment and dependences.

## Set up a new conda environment with Python 3.8.19
conda create -n BNNCC python=3.8.19
conda activate BNNCC

## Install python libraries or dependences.
# pip install gcastle==1.0.3 torch==2.1.0 graphviz==0.20.3 configargparse==1.7 jupyter==1.1.1 lazypredict==0.2.13 tensorflow==2.13.1
pip install -r requirements.txt

• Evaluation: quick start.

python main_IHDP.py  # Experiments on the IHDP dataset

📚 Citation

Please cite our work if you found the resources in this repository useful:

@article{cai2026causal,
  title={Causal Structure-Enhanced Branch Neural Networks for Interpretable and Robust Regression},
  author={Cai, Jiangqian and Qian, Quan},
  journal={Expert Systems with Applications},
  pages={131851},
  year={2026},
  publisher={Elsevier}
}

🥰 Acknowledgements

We would like to express our sincere gratitude to the related works and open-source codes that have served as inspiration for our project:

• Gcastle package. [github]

• NNSIP package. [github]

• Lazypredict package. [github]