Fast, principled graph discovery for causal scientists and ML practitioners, powered by the algorithms in Recursive Causal Discovery (JMLR 2025).

RCD is a batteries-included Python toolkit for learning causal skeletons from observational data. It ships the exact implementations from our JMLR paper—RSL-D/W, L-MARVEL, MARVEL, and the ROL hill-climbing refinements—plus the utilities you need to drop them into real pipelines: conditional-independence (CI) tests, Markov-boundary estimators, synthetic-data generators, and ready-to-run demos.

Install
pip install rcd

1. Highlights
2. Algorithms inside
3. Quickstart
4. Choose your CI test
5. Demos & docs
6. Roadmap & contributing
7. How to cite
8. License

• State-of-the-art guarantees – Implementations follow the proofs and numbering of Recursive Causal Discovery (JMLR 26:61) verbatim.
• Swappable CI tests – Fisher-Z, Pearson residuals, a battery of power-divergence tests, or your own callable with signature (x_idx, y_idx, cond_set, data).
• Markov-boundary aware – Efficient Gaussian estimators out of the box plus hooks for custom routines.
• Examples that actually run – Each algorithm ships with a runnable script in examples/ demonstrating realistic settings and reporting precision/recall/F1.
• Reproducible utilities – Synthetic DAG generators, F1 helpers, clique-number estimation, and more so you can benchmark methods in minutes.

Every algorithm exposes the same high-level API:

learned_skeleton = algo.learn_and_get_skeleton(
    ci_test=my_ci_function,
    data=data_matrix_or_dataframe,
    **optional_kwargs,
)

ci_test is any callable with the signature (x_idx: int, y_idx: int, cond_set: list[int], data: np.ndarray | pd.DataFrame) -> bool, returning True when the variables are conditionally independent.

import networkx as nx
import numpy as np
from rcd import rsl_d
from rcd.utilities.ci_tests import fisher_z
from rcd.utilities.data_graph_generation import gen_er_dag_adj_mat, gen_gaussian_data
from rcd.utilities.utils import f1_score_edges
np.random.seed(2308)
n = 60
p = n ** (-0.85)
adj_mat = gen_er_dag_adj_mat(n, p)
data = gen_gaussian_data(adj_mat, 5_000)
ci_test = lambda x, y, z, d: fisher_z(x, y, z, d, significance_level=2 / n**2)
learned = rsl_d.learn_and_get_skeleton(ci_test, data)
true_skeleton = nx.from_numpy_array(adj_mat, create_using=nx.Graph)
precision, recall, f1 = f1_score_edges(true_skeleton, learned, return_only_f1=False)
print(f"Precision={precision:.3f}, Recall={recall:.3f}, F1={f1:.3f}")

Want bound-clique graphs instead? Swap rsl_d for rsl_w and pass clique_num=get_clique_number(nx_graph).

All CI tests live under rcd.utilities.ci_tests:

• fisher_z – Gaussian Fisher-Z test (default in our paper).
• pearsonr – Partial correlation via linear regression residuals.
• chi_square, g_sq, freeman_tuckey, neyman, cressie_read, modified_log_likelihood – members of the power-divergence family supporting discrete data.
• get_perfect_ci_test(adj_matrix) – Oracle test derived from ground-truth adjacency, great for debugging.

Because every test shares the same function signature you can mix and match without touching the algorithm code.

• Run the demos – python examples/rsl/rsl_d_demo.py, python examples/l_marvel/l_marvel_demo.py, etc. Each prints runtime plus precision/recall/F1, and the RSL-W demo even plots the learned skeleton.
• API reference – See the module docstrings (rcd/rsl/*.py, rcd/rol/rol_hc.py, rcd/l_marvel/l_marvel.py) for NumPy-style documentation and theorem references tied to the JMLR paper.
• Website – https://rcdpackage.com hosts rendered docs and tutorials.
• GitHub – https://github.com/ban-epfl/rcd houses the full source, issues, and release history.

We are actively working on:

1. Meek rule orientation – Extending the recursive learners with Meek rules to orient as many edges as possible.
2. CPDAG outputs – Returning completed partially directed acyclic graphs (CPDAGs) instead of bare skeletons.

Pull requests are welcome—especially those that add new CI tests or improve coverage. Please open an issue describing the improvement, follow our NumPy-style typing/docstring conventions, and run pytest plus the relevant demos before submitting.

If you build on RCD, please cite our JMLR article:

Mokhtarian, E., Elahi, S., Akbari, S., & Kiyavash, N. (2025). Recursive Causal Discovery. Journal of Machine Learning Research, 26(61), 1–65. https://www.jmlr.org/papers/v26/24-0384.html

@article{JMLR:v26:24-0384,
  author  = {Ehsan Mokhtarian and Sepehr Elahi and Sina Akbari and Negar Kiyavash},
  title   = {Recursive Causal Discovery},
  journal = {Journal of Machine Learning Research},
  year    = {2025},
  volume  = {26},
  number  = {61},
  pages   = {1--65},
  url     = {https://www.jmlr.org/papers/v26/24-0384.html}
}

RCD is distributed under the BSD 2-Clause License.

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