GnIES Algorithm for Causal Discovery

This repository contains a python implementation of the GnIES algorithm from the paper "Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions" by Juan L. Gamella, Armeen Taeb, Christina Heinze-Deml and Peter Bühlmann.

If you find this code useful, please consider citing:

@article{gamella2022characterization,
  title={Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions},
  author={Gamella, Juan L. and Taeb, Armeen and Heinze-Deml, Christina and B\"uhlmann, Peter},
  journal={arXiv preprint arXiv:2211.14897},
  year={2022}
}

Installation

You can clone this repo or install the python package via pip:

pip install gnies

There was an effort to keep dependencies on other packages to a minimum. As a result the package only depends on numpy and ges (with the former being the only dependency of the latter).

Running the algorithm

GnIES can be run through the function gnies.fit:

def fit(
    data,
    lmbda=None,
    known_targets=set(),
    approach="greedy",
    # Parameters used for greedy approach
    I0=set(),
    phases=["forward", "backward"],
    # Parameters used for rank approach
    direction="forward",
    center=True,
    # Parameters used by inner-procedure (modified GES)
    ges_iterate=True,
    ges_phases=["forward", "backward", "turning"],
    debug=0
)

A detailed documentation can be found in the function's docstring. The most important parameters are:

• data (list of numpy.ndarray): A list with the samples from the different environments, where each sample is an array with columns corresponding to variables and rows to observations.
• lmbda (float, default=None): The penalization parameter for the penalized-likelihood score. If None, the BIC penalization is chosen, that is, 0.5 * log(N) where N is the total number of observations from all environments.
• approach ({'greedy', 'rank'}, default='greedy'): The approach used by the outer procedure of GnIES. With 'greedy' targets are added and/or removed until the score does not improve; this corresponds to the results from figures 1,2 and 3 in the paper. With 'rank', the faster ranking procedure is run, at a small cost in the accuracy of the estimates (see figure 7 in the paper). The two procedures are implemented in gnies.main.fit_greedy and gnies.main.fit_rank, respectively.
• center (bool, default=True): Whether GnIES considers interventions on only the noise-term variance (center=True, i.e., data is centered before computing the score) or on both the mean and variance (center=False). The identifiability results in the paper correspond to (center=True), but (center=False) may improve power in some scenarios.

Example using the greedy approach

Here sempler is used to generate interventional data from a Gaussian SCM, but is not a dependency of the package.

import sempler, sempler.generators
import gnies

# Generate a random SCM using sempler
W = sempler.generators.dag_avg_deg(10, 2.1, 0.5, 1, random_state=42)
scm = sempler.LGANM(W, (0, 0), (1, 2), random_state=42)

# Generate interventional data
n = 1000
data = [
    scm.sample(n, random_state=42),
    scm.sample(n, noise_interventions={1: (0, 11)}, random_state=42),
    scm.sample(n, noise_interventions={2: (0, 12), 3: (0, 13)}, random_state=42),
]

# Run GnIES
_score, icpdag, I = gnies.fit(data)
print(icpdag, I)

# Output:
# [[0 1 0 0 0 1 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]
#  [0 1 0 0 0 0 0 0 0 0]
#  [0 1 0 0 0 0 1 0 0 1]
#  [1 0 1 0 0 0 0 0 0 0]
#  [0 1 1 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 1 0 0 1]
#  [0 1 0 1 0 0 1 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]] {1, 2, 3}

Example using the faster ranking approach

# Run GnIES (on the same data as above)
_score, icpdag, I = gnies.fit(data, approach='rank')
print(icpdag, I)

# Output:
# [[0 1 0 0 0 1 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]
#  [0 1 0 0 0 0 0 0 0 0]
#  [0 1 0 0 0 0 1 0 0 1]
#  [1 0 1 0 0 0 0 0 0 0]
#  [0 1 1 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 1 0 0 1]
#  [0 1 0 1 0 0 1 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0]] {1, 2, 3}

Code Structure

The source code modules can be found inside the gnies/ directory. These include:

• gnies.main which is the main module with the calls to start GnIES.
• gnies.utils contains auxiliary functions and the modified completion algorithm to transform PDAGs into a I-CPDAG, in the function pdag_to_icpdag.
• scores/ contains the modules with the score classes:
  • ges.scores.decomposable_score contains the base class for decomposable score classes (see that module for more details).
  • ges.scores.gnies_score contains an implementation of the cached GnIES score, as described in section 4 of the paper.
• test/ contains the unit tests of the scores and other components.

Tests

All components come with unit tests to match, and some property-based tests. Of course, this doesn't mean there are no bugs, but hopefully it means they are less likely :)

The tests can be run with make test. You can add SUITE=<module_name> to run a particular module only. There is, however, the additional dependency of the sempler package to run the tests. You can find the details in requirements_tests.txt.

Feedback

I hope you find this useful! Feedback and (constructive) criticism is always welcome, just shoot me an email :)