Skip to content

❓y0 (pronounced "why not?") is for causal inference in Python


Notifications You must be signed in to change notification settings


Repository files navigation


Tests Cookiecutter template from @cthoyt PyPI PyPI - Python Version PyPI - License Documentation Status DOI Code style: black

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[A](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(
        (Z2, Z1),
        (Z1, X),
        (X, Y),
        (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* Shpitser and Pearl, 2012
IDC* Shpitser and Pearl, 2012
Surrogate Outcomes Tikka and Karvanen, 2018

Apply an algorithm to an 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 Identification, identify

# TODO after ID* and IDC* are done, we'll update this interface
query = Identification.from_expression(graph=napkin, query=P(Y @ X))
estimand = identify(query)
assert estimand == P(Y @ X)

🚀 Installation

The most recent release can be installed from PyPI with:

$ pip install y0

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

$ pip install git+

👐 Contributing

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

👋 Attribution

⚖️ License

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

📖 Citation

Before we publish an application note on y0, you can cite this software via our Zenodo record (also see the badge above):

  author       = {Charles Tapley Hoyt and
                  Jeremy Zucker and
                  Marc-Antoine Parent},
  title        = {y0-causal-inference/y0},
  month        = jun,
  year         = 2021,
  publisher    = {Zenodo},
  version      = {v0.1.0},
  doi          = {10.5281/zenodo.4950768},
  url          = {}

🙏 Supporters

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

💰 Funding

The development of the Y0 Causal Inference Engine has been funded 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-python-package template.

🛠️ Development

See developer instructions

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

Developer Installation

To install in development mode, use the following:

$ git clone git+
$ cd y0
$ pip install -e .

❓ Testing

After cloning the repository and installing tox with pip install tox, the unit tests in the tests/ folder can be run reproducibly with:

$ tox

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

📦 Making a Release

After installing the package in development mode and installing tox with pip install tox, the commands for making a new release are contained within the finish environment in tox.ini. Run the following from the shell:

$ tox -e finish

This script does the following:

  1. Uses BumpVersion to switch the version number in the setup.cfg and src/y0/ to not have the -dev suffix
  2. Packages the code in both a tar archive and a wheel
  3. Uploads to PyPI using twine. Be sure to have a .pypirc file configured to avoid the need for manual input at this step
  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.