BHIP

This repo provides an implementation of Bayesian Hierarchical Invariant Prediction (BHIP) and experimental results from the paper Bayesian Hierarchical Invariant Prediction (arXiv:2505.11211 [stat.ML]).

The BHIP algorithm is implemented in src/, using NumPyro for probabilistic modeling.

Structure

• src/ — core BHIP algorithm: hierarchical models and invariance tests
• experiments/ — all experiments organized by paper section:
  • bus_dwelling/ — Section 4.1: bus dwelling time case study (synthetic data, generated in notebook)
  • educational_attainment/ — Section 4.2: school achievement case study, including Appendix E sparse priors
  • computational_study/ — Section 4.3: computational complexity comparison (ICP vs BHIP)
  • synthetic_benchmark/ — Section 4.4.1: low-dimensional synthetic benchmark and sensitivity analysis (Appendix H, I)
  • gene_perturbation/ — Section 4.4.2: Kemmeren yeast gene perturbation benchmark
• external/ — git submodule for the BIP baseline

Setup

Clone with submodules to include the BIP baseline:

git clone --recurse-submodules https://github.com/fmfsa/bhip

Install dependencies:

pip install -r requirements_cpu.txt

Data

• Bus dwelling (Section 4.1) — synthetic, generated within the notebook.
• Educational attainment (Section 4.2) — CollegeDistance dataset from the R package AER (Rouse, 1995), downloaded automatically by the notebook.
• Synthetic benchmarks (Sections 4.3, 4.4.1) — generated by the experiment scripts using sempler.
• Kemmeren gene perturbation (Section 4.4.2) — yeast gene deletion data from Kemmeren et al. (2014). Download Kemmeren.hdf5 from the deleteome database and run experiments/gene_perturbation/extract_data.py to generate the required CSV and text files.

Citing

If you find this code helpful, please cite:

@InProceedings{madaleno2026,
  title =        {Bayesian Hierarchical Invariant Prediction},
  author =       {Francisco Madaleno and Pernille Julie Viuff Sand and Francisco C. Pereira and Sergio Hernan Garrido Mejia},
  booktitle =    {Proceedings of the Fifth Conference on Causal Learning and Reasoning},
  year =         {2026},
  editor =       {Bijan Mazaheri and Niels Richard Hansen},
  series =       {Proceedings of Machine Learning Research},
  month =        {Apr},
  publisher =    {PMLR},
}