y0

y0 (pronounced "why not?") is Python code for causal inference.

💪 Getting Started

Representing Probability Expressions

y0 has a fully featured internal domain specific language for representing probability expressions:

from y0.dsl import P, A, B

# The probability of A given B
expr_1 = P(A | B)

# The probability of A given not B
expr_2 = P(A | ~B)

# The joint probability of A and B
expr_3 = P(A, B)

It can also be used to manipulate expressions:

from y0.dsl import P, A, B, Sum

P(A, B).marginalize(A) == Sum[A](P(A, B))
P(A, B).conditional(A) == P(A, B) / Sum[B](P(A, B))

DSL objects can be converted into strings with str() and parsed back using y0.parser.parse_y0().

A full demo of the DSL can be found in this Jupyter Notebook

Representing Causality

y0 has a notion of acyclic directed mixed graphs built on top of networkx that can be used to model causality:

from y0.graph import NxMixedGraph
from y0.dsl import X, Y, Z1, Z2

# Example from:
#   J. Pearl and D. Mackenzie (2018)
#   The Book of Why: The New Science of Cause and Effect.
#   Basic Books, p. 240.
napkin = NxMixedGraph.from_edges(
    directed=[
        (Z2, Z1),
        (Z1, X),
        (X, Y),
    ],
    undirected=[
        (Z2, X),
        (Z2, Y),
    ],
)

y0 has many pre-written examples in y0.examples from Pearl, Shpitser, Bareinboim, and others.

do Calculus

y0 provides actual implementations of many algorithms that have remained unimplemented for the last 15 years of publications including:

Algorithm	Reference
ID	Shpitser and Pearl, 2006
IDC	Shpitser and Pearl, 2008
ID Star	Shpitser and Pearl, 2012
IDC Star	Shpitser and Pearl, 2012
Surrogate Outcomes	Tikka and Karvanen, 2018
Counterfactual Transportability	Correia, Lee, Bareinboim, 2022

Apply an algorithm to an Acyclic Directed Mixed Graph (ADMG) and a causal query to generate an estimand represented in the DSL like:

from y0.dsl import P, X, Y
from y0.examples import napkin
from y0.algorithm.identify import identify_outcomes

estimand = identify_outcomes(napkin, treatments=X, outcomes=Y)
assert estimand == P(Y | X)

🚀 Installation

The most recent release can be installed from PyPI with uv:

$ uv pip install y0

or with pip:

$ python3 -m pip install y0

The most recent code and data can be installed directly from GitHub with uv:

$ uv pip install git+https://github.com/y0-causal-inference/y0.git

or with pip:

$ python3 -m pip install git+https://github.com/y0-causal-inference/y0.git

👐 Contributing

Contributions, whether filing an issue, making a pull request, or forking, are appreciated. See CONTRIBUTING.md for more information on getting involved.

👋 Attribution

⚖️ License

The code in this package is licensed under the BSD-3-Clause license.

📖 Citation

Causal identification with Y0
Hoyt, C.T., et al. (2025) arXiv, 2508.03167

@software{hoyt2025y0,
    title = {Causal identification with $Y_0$},
    author = {Charles Tapley Hoyt and Craig Bakker and Richard J. Callahan and Joseph Cottam and August George and Benjamin M. Gyori and Haley M. Hummel and Nathaniel Merrill and Sara Mohammad Taheri and Pruthvi Prakash Navada and Marc-Antoine Parent and Adam Rupe and Olga Vitek and Jeremy Zucker},
    year = {2025},
    eprint = {2508.03167},
    archivePrefix = {arXiv},
    primaryClass = {cs.AI},
    url = {https://doi.org/10.48550/arXiv.2508.03167},
    doi = {10.48550/arXiv.2508.03167},
}

🎁 Support

This project has been supported by several organizations (in alphabetical order):

• Biopragmatics Lab
• Gyori Lab for Computational Biomedicine
• Harvard Program in Therapeutic Science - Laboratory of Systems Pharmacology
• Pacific Northwest National Laboratory

💰 Funding

This project has been supported by the following grants:

Funding Body	Program	Grant
DARPA	Automating Scientific Knowledge Extraction (ASKE)	HR00111990009
PNNL Data Model Convergence Initiative	Causal Inference and Machine Learning Methods for Analysis of Security Constrained Unit Commitment (SCY0)	90001
DARPA	Automating Scientific Knowledge Extraction and Modeling (ASKEM)	HR00112220036

🍪 Cookiecutter

This package was created with @audreyfeldroy's cookiecutter package using @cthoyt's cookiecutter-snekpack template.

🛠️ For Developers

See developer instructions

The final section of the README is for if you want to get involved by making a code contribution.

Development Installation

To install in development mode, use the following:

$ git clone git+https://github.com/y0-causal-inference/y0.git
$ cd y0
$ uv pip install -e .

Alternatively, install using pip:

$ python3 -m pip install -e .

🥼 Testing

After cloning the repository and installing tox with uv tool install tox --with tox-uv or python3 -m pip install tox tox-uv, the unit tests in the tests/ folder can be run reproducibly with:

$ tox -e py

Additionally, these tests are automatically re-run with each commit in a GitHub Action.

📖 Building the Documentation

The documentation can be built locally using the following:

$ git clone git+https://github.com/y0-causal-inference/y0.git
$ cd y0
$ tox -e docs
$ open docs/build/html/index.html

The documentation automatically installs the package as well as the docs extra specified in the pyproject.toml. sphinx plugins like texext can be added there. Additionally, they need to be added to the extensions list in docs/source/conf.py.

The documentation can be deployed to ReadTheDocs using this guide. The .readthedocs.yml YAML file contains all the configuration you'll need. You can also set up continuous integration on GitHub to check not only that Sphinx can build the documentation in an isolated environment (i.e., with tox -e docs-test) but also that ReadTheDocs can build it too.

🧑‍💻 For Maintainers

See maintainer instructions

Initial Configuration

Configuring ReadTheDocs

ReadTheDocs is an external documentation hosting service that integrates with GitHub's CI/CD. Do the following for each repository:

1. Log in to ReadTheDocs with your GitHub account to install the integration at https://readthedocs.org/accounts/login/?next=/dashboard/
2. Import your project by navigating to https://readthedocs.org/dashboard/import then clicking the plus icon next to your repository
3. You can rename the repository on the next screen using a more stylized name (i.e., with spaces and capital letters)
4. Click next, and you're good to go!

Configuring Archival on Zenodo

Zenodo is a long-term archival system that assigns a DOI to each release of your package. Do the following for each repository:

1. Log in to Zenodo via GitHub with this link: https://zenodo.org/oauth/login/github/?next=%2F. This brings you to a page that lists all of your organizations and asks you to approve installing the Zenodo app on GitHub. Click "grant" next to any organizations you want to enable the integration for, then click the big green "approve" button. This step only needs to be done once.
2. Navigate to https://zenodo.org/account/settings/github/, which lists all of your GitHub repositories (both in your username and any organizations you enabled). Click the on/off toggle for any relevant repositories. When you make a new repository, you'll have to come back to this

After these steps, you're ready to go! After you make "release" on GitHub (steps for this are below), you can navigate to https://zenodo.org/account/settings/github/repository/y0-causal-inference/y0 to see the DOI for the release and link to the Zenodo record for it.

Registering with the Python Package Index (PyPI)

The Python Package Index (PyPI) hosts packages so they can be easily installed with pip, uv, and equivalent tools.

1. Register for an account here
2. Navigate to https://pypi.org/manage/account and make sure you have verified your email address. A verification email might not have been sent by default, so you might have to click the "options" dropdown next to your address to get to the "re-send verification email" button
3. 2-Factor authentication is required for PyPI since the end of 2023 (see this blog post from PyPI). This means you have to first issue account recovery codes, then set up 2-factor authentication
4. Issue an API token from https://pypi.org/manage/account/token

This only needs to be done once per developer.

Configuring your machine's connection to PyPI

This needs to be done once per machine.

$ uv tool install keyring
$ keyring set https://upload.pypi.org/legacy/ __token__
$ keyring set https://test.pypi.org/legacy/ __token__

Note that this deprecates previous workflows using .pypirc.

📦 Making a Release

Uploading to PyPI

After installing the package in development mode and installing tox with uv tool install tox --with tox-uv or python3 -m pip install tox tox-uv, run the following from the console:

$ tox -e finish

This script does the following:

1. Uses bump-my-version to switch the version number in the pyproject.toml, CITATION.cff, src/y0/version.py, and docs/source/conf.py to not have the -dev suffix
2. Packages the code in both a tar archive and a wheel using uv build
3. Uploads to PyPI using uv publish.
4. Push to GitHub. You'll need to make a release going with the commit where the version was bumped.
5. Bump the version to the next patch. If you made big changes and want to bump the version by minor, you can use tox -e bumpversion -- minor after.

Releasing on GitHub

1. Navigate to https://github.com/y0-causal-inference/y0/releases/new to draft a new release
2. Click the "Choose a Tag" dropdown and select the tag corresponding to the release you just made
3. Click the "Generate Release Notes" button to get a quick outline of recent changes. Modify the title and description as you see fit
4. Click the big green "Publish Release" button

This will trigger Zenodo to assign a DOI to your release as well.

Updating Package Boilerplate

This project uses cruft to keep boilerplate (i.e., configuration, contribution guidelines, documentation configuration) up-to-date with the upstream cookiecutter package. Install cruft with either uv tool install cruft or python3 -m pip install cruft then run:

$ cruft update

More info on Cruft's update command is available here.