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A library for constraint-based causal structure learning on GPUs.

Project description

Python tests + coverage test benchmarks test cuda lint python lint cuda


GPUCSL is a python library for constraint-based causal structure learning using Graphics Processing Units (GPUs). In particular, it utilizes CUDA for GPU acceleration to speed up the well-known PC algorithm.


  • Performant GPU implementation of the PC algorithm (covers discrete, and multivariate normal distributed data), see General Notes;
  • Multi-GPU support (experimental; for now, only for gaussian CI kernel);
  • Easy to install and use, see Usage;
  • A Command Line Interface (CLI);
  • Modular, extensible, tested thoroughly.

General Notes

GPUCSL enables the GPU-accelerated estimation of the equivalence class of a data generating Directed Acyclic Graph (DAG) from observational data via constraint-based causal structure learning, cf. Kalisch et al. [^Kalisch] or Colombo and Maathuis [^Colombo]. Within the equivalence class, all DAGs have the same skeleton and the same v-structures and they can be uniquely represented by a Completely Partially Directed Acyclic Graph (CPDAG). In this context, GPUCSL implements the fully order-independent version of the PC algorithm, called PC-stable, to estimate the CPDAG under common faithfulness and sufficiency assumptions, see Colombo and Maathuis [^Colombo]. Hence, the implementation follows the pc-function within the R-package pcalg (For more information, see the pcalg-Documentation). In particular, in the case of conflicts within the orientation phase, conflicts are solved similar to the pc within the pcalg implementation and yield matching results.

Note, that GPUCSL provides kernel implementations that cover conditional independence (CI) tests for discrete distributed data according to the ideas of Hagedorn and Huegle[^HagedornDiscrete]. Implementation of the CI tests for multivariate normal (or Gaussian) distributed data follows the ideas of Schmidt et al. [^SchmidtGaussian] and Zarebavani et al. [^ZarebavaniCupc].


Linux and a NVIDIA GPU with CUDA are required. We support running on multiple GPUs (experimental; for now, only for Gaussian CI kernel - GaussianPC).


With the CLI, the PC algorithm is executed on the specified datasets. Three output files will be written to the specified directory:

  • {dataset}.gml - the resulting CPDAG containing the causal relationships
  • {dataset}_pmax.csv - the maximum pvalues used for the conditional independence tests
  • {dataset}_sepset.csv - the separation sets for the removed edges
  • {dataset}_config.txt - the parameters the CLI got called with

All paths you give to the CLI are relative to your current directory. An example call for GPUCSL with a CI test for multivariate normal or Gaussian distributed data could look like this (assuming your data is in "./data.csv"):

python3 -m gpucsl --gaussian -d ./data.csv -o . -l 3

Python API

GPUCSL provides a python API for:

  • GaussianPC - implements the full PC algorithm for multivariate normal data. Outputs the CPDAG from observational data. Similar to the CLI.
  • DiscretePC -implements the full PC algorithm for discrete data. Outputs the CPDAG from observational data. Similar to the CLI.
  • discover_skeleton_gpu_gaussian - determines the undirected skeleton graph for gaussian distribution
  • discover_skeleton_gpu_discrete - determines the undirected skeleton graph for discrete distribution
  • orient_edges - orients the edges of the undirected skeleton graph by detection of v-structures and application of Meek's orientation rules. Outputs the CPDAG from skeleton.

Additional detail is found in the API description.

The following code snippet provides a small example for using GaussianPC:

import numpy as np
from gpucsl.pc.pc import GaussianPC

samples = np.random.rand(1000, 10)
max_level = 3
alpha = 0.05
((directed_graph, separation_sets, pmax, discover_skeleton_runtime,
  edge_orientation_runtime, discover_skeleton_kernel_runtime),
    pc_runtime) = GaussianPC(samples,

Additional usage examples can be found in docs/examples/.

Multi GPU support

Multi GPU support is currently only implemented for the gaussian CI kernel (GaussianPC) for skeleton discovery. The adjacency matrix (skeleton) is partitioned horizontally, and each GPU executes the CI tests on the assigned partition. For example, in the case of the dataset with 6 variables and 3 GPUs, the first GPU executes CI tests on edges 0-i, 1-i, where i is in {0..5} (0-indexing), the second GPU executes CI tests on edges 2-i, 3-i and so on.

In case of an edge being deleted on multiple GPUs in the same level (for example, the edge 1-3 is deleted on the first GPU, the edge 3-1 is deleted on the second GPU in the example above), the separation set with the highest p-value is written to the end result (along with the corresponding p-value).


How to use with docker

First install Docker (for instructions refer to: Please remember: you will still need a NVIDIA GPU and the CUDA Toolkit installed to used the Docker image.

The current dockerfiles are written with CUDA version 11.2 as a target. Should your host system have a different version installed (you can look it up by running nvidia-smi -q -u and look for CUDA Version), you should go into the dockerfile and change the version in line 1 (the from statement) and in line 29 where the correct cupy version is installed.

To just use gpucsl:

docker build --target gpucsl -t gpucsl .
docker run --runtime=nvidia --gpus all -i -t gpucsl

If you want to upload/download files from/to the container run (to get the container id look it up by: docker container ps):

# upload your-file.txt to container from the current directory into the directory where gpucsl is installed
docker cp your-file.txt container_id:/gpucsl/your-file.txt

# download your-file.txt from container where gpucsl is installed to current directory
docker cp container_id:/gpucsl/your-file.txt your-file.txt

If you want to run the benchmarks:

docker build --target gpucsl-benchmarks -t benchmarks .
docker run --runtime=nvidia --gpus all -i -t benchmarks

Full CLI Documentation

The following options are available:

Shorthand Longform Description
--gaussian Executes Fisher’s z-transformed (partial) correlation-based CI test for multvariate normal (or Gaussian) distributed data; Either this or discrete have to be set!
--discrete Executes Pearson’s χ2 CI test for discrete distributed data; Either this or gaussian have to be set!
-a --alpha Sets the alpha level for PC algorithm to use. Default is 0.05.
-b --debug Is a flag for debugging the kernels. When activated kernels get compiled with debug flag and lineinfo enabled.
-c --correlation-matrix Defines the path to a cached correlation matrix file in csv format. You still have to give a dataset (-d/--dataset option)!
-d --dataset (required) Defines the path to your input data in csv format; Is relative to your current directory
-h --help shows a list and a sort explanation of all available options
-g --gpus Indices of GPUs that should be used for independence test calculation (currently only supported for gaussian independence test). When not specified will use all available GPUs.
-l --max-level Gives the max level for the PC algorithm (level of the pc algorithm is <= max level)
-o --output-directory (required) Defines the output directory; Is relative to your current directory
-s --sync-device Index of the GPU used to sync the others (currently only supported for gaussian independence test). Default is 0
-v Prints verbose output
-vv Prints debug output


Dependencies setup

  • Clone the repo
  • From the project dir, call ./scripts/ (see section in scripts) to download the data folder from dropbox. It contains several example/test datasets.
  • It is recommended to use a virtual environment: python3 -m venv venv && source venv/bin/activate (in bash, zsh).
  • Upgrade pip and install build: python3 -m pip install --upgrade pip build.
  • Make sure to install the cuda toolkit and cupy (see installation).
  • Run pip install . to install the release package.
  • Run pip install -e "./[dev]" to also install for development, with dev dependencies.

Linting Setup

  • Install clang-tidy and clang-format sudo apt install clang-format, sudo apt install clang-tidy.
  • Set up git to use our hooks git config --local core.hooksPath .githooks/ to execute lint checks on pushing.
  • You can manually lint code with ./scripts/ and ./scripts/
  • You can autofix code with ./scripts/ --fix and ./scripts/ --fix.
  • Import .vscode/settings.json if you use vscode. This sets up VSCode to automatically run black and clang-format (respectively) on save.

Building a Package

  • Build sdist: python3 -m build.
  • Build for dev: python3 -m pip install --editable . (installs it locally).

Running Tests

  • Make sure to have your python environment activated and run python3 -m pip install -e "./[dev]".
  • Run python tests: pytest (or in VSCode go to "Testing").
  • There are additional flags:
    • for tests that take a long time and end-to-end tests from installation to CLI call, there is pytest --run_slow;
    • for CI only tests, there is pytest --run_testPyPI.
  • Run cuda tests: ./scripts/

Release a new version using the github action

  • Bump the version in setup.cfg and commit your change to main.
  • On this commit, create a new tag (e.g., git tag v0.0.1 and git push origin v0.0.1)
  • Go to and create a new release for this tag with the same name as the version.
  • A github action will run on release and first test this deployment on testPyPi and then publish the library to pypi.

Manually publish to PyPi

python3 -m pip install --upgrade build twine
python3 -m build
# Upload to testPyPi
# use __token__ as username and the pypi token as password
python3 -m twine upload --repository testpypi dist/*
# Upload to PyPi
python3 -m twine upload dist/*


We provide some helper scripts for data generation, testing, and benchmarking.

To run some of the scripts below, a working R installation is required.

R setup

An R installation with the following packages is needed. These steps were tested with R 4.1.2 on Ubuntu 20.04.3 LTS.

apt install -y r-cran-fastica
apt install -y libv8-3.14-dev
apt install -y libcurl4-openssl-dev
apt install -y libgmp3-dev
  • install R packages // TODO RScript to be tested
BiocManager::install(version = "3.14")
BiocManager::install(c("graph", "RBGL", "Rgraphviz"))


This can be used to run the R-package pcalg on test data and output its results (as comparison for gpucsl). Some of the outputs are already contained in the data folder.

Usage (make sure to do the call from the top-level project folder):

  • ./scripts/use_pcalg_gaussian.R {dataset};
  • for example: ./scripts/use_pcalg_gaussian.R NCI-60.

Assumes that "NCI-60" folder lies in the data folder, also works for all other datasets in data.

Call this script once to download all test data from a dropbox folder (without having to generate some parts of it yourself which can take a long time). It will create a data folder. Please check dataset license information in dropbox before downloading.


This script can be used to generate discrete test data using the R-package bnlearn. The outputs necessary for the package tests can be generated by ./, which internally calls this script. The data needs to be in the data folder. Usage:

  • Rscript use_bnlearn_discrete.r {dataset_name} {maximum_level};
  • for example: Rscript use_bnlearn_discrete.r alarm 3.

Make sure to do the call from the scripts folder.

This is a simple wrapper around sklearn's OrdinalEncoder to allow csv data that is not already encoded to be loaded into the library. Usage:

  • python3 -m {dataset_name};
  • for example: python3 -m alarm.


  • To execute, run ./benchmarks/
    • The script will tell you the output folder where it wrote the benchmark run results. It automatically installs R dependencies. You can also specify which benchmarks to run in the first parameter.
    • To run the benchmarks, you have to place the cupc repo in the benchmarks/cupc subdirectory. A forked version with timing annotations is available at
  • Once completed, open benchmarks/visualization notebooks (e.g. in VSCode just open the file, for instructions see In the notebook, specify the benchmark results folder (the one from step 1) and run all cells.


  • Tom Braun (@BraunTom)
  • Christopher Hagedorn (@ChristopherSchmidt89)
  • Johannes Huegle (@JohannesHuegle)
  • Ben Hurdelhey (@benrobby)
  • Dominik Meier (@XPerianer)
  • Petr Tsayun (@PeterTsayun)


This project is licensed under the MIT license (see LICENSE.txt) unless otherwise noted in the respective source files:

  • gpucsl/pc/;

For the license information of datasets, please check in dropbox before downloading datasets.


[^Kalisch]: Kalisch M., Mächler M., Colombo D., Maathuis M.H., Bühlmann P. (2012). "Causal Inference Using Graphical Models with the R Package pcalg." Journal of Statistical Software, 47(11), pp. 1–26. [^Colombo]: Colombo D., and Maathuis, M.H. (2014). "Order-independent constraint-based causal structure learning." Journal of Machine Learning Research 15 3921-3962. [^HagedornDiscrete]: Hagedorn, C., and Huegle, J. (2021). "GPU-Accelerated Constraint-Based Causal Structure Learning for Discrete Data." Proceedings of the 2021 SIAM International Conference on Data Mining (SDM). pp. 37–45. [^SchmidtGaussian]: Schmidt, C., Huegle, J., and Uflacker, M. (2018). "Order-independent constraint-based causal structure learning for gaussian distribution models using GPUs." Proceedings of the 30th International Conference on Scientific and Statistical Database Management (SSDBM). pp. 19:1–19:10. [^ZarebavaniCupc]: Zarebavani, B., Jafarinejad, F., Hashemi, M., & Salehkaleybar, S. (2020). cuPC: CUDA-Based Parallel PC Algorithm for Causal Structure Learning on GPU. IEEE Transactions on Parallel and Distributed Systems, 31(3), 530–542.

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