LiNGAM is a new method for estimating structural equation models or linear Bayesian networks. It is based on using the non-Gaussianity of the data.

• The LiNGAM Project

📦 Requirements

• Python3
• numpy
• scipy
• scikit-learn
• graphviz
• statsmodels
• networkx
• pandas
• itertools
• semopy
• autograd

🛠️ Installation

To install lingam package, use pip as follows:

pip install lingam

🚀 Usage

import numpy as np
import pandas as pd
import lingam

# To run causal discovery, we create a DirectLiNGAM object and call the fit method.
model = lingam.DirectLiNGAM()
model.fit(X)

# Using the causal_order_ properties,
# we can see the causal ordering as a result of the causal discovery.
print(model.causal_order_)

# Also, using the adjacency_matrix_ properties,
# we can see the adjacency matrix as a result of the causal discovery.
print(model.adjacency_matrix_)

📚 Documentation

Tutorial and API reference

Tutorial slides

💡 Examples

We provide several examples of running the LiNGAM algorithm in Jupyter Notebook. lingam/examples

📄 License

This project is licensed under the terms of the MIT license.

🤝 Contribution

For guidelines how to contribute to lingam package, take a look at CONTRIBUTING.md.

📖 References

Package

If you find our package useful, please cite the following paper:

• T. Ikeuchi, M. Ide, Y. Zeng, T. N. Maeda, and S. Shimizu. Python package for causal discovery based on LiNGAM. Journal of Machine Learning Research, 24(14): 1−8, 2023. [PDF]

Basic DAG model

Should you use this package for performing ICA-based LiNGAM algorithm, we kindly request you to cite the following paper:

• S. Shimizu, P. O. Hoyer, A. Hyvärinen, and A. Kerminen. A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7: 2003--2030, 2006. [PDF]

Should you use this package for performing DirectLiNGAM algorithm, we kindly request you to cite the following two papers:

• S. Shimizu, T. Inazumi, Y. Sogawa, A. Hyvärinen, Y. Kawahara, T. Washio, P. O. Hoyer and K. Bollen. DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. Journal of Machine Learning Research, 12(Apr): 1225--1248, 2011. [PDF]
• A. Hyvärinen and S. M. Smith. Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. Journal of Machine Learning Research, 14(Jan): 111--152, 2013. [PDF]

Should you use this package for performing RESIT algorithm, we kindly request you to cite the following paper:

• J. Peters, J. M. Mooij, D. Janzing, and B. Schölkopf. Causal Discovery with Continuous Additive Noise Models. Journal of Machine Learning Research, 15(58): 2009--2053, 2014. [PDF]

Should you use this package for performing GroupDirectLiNGAM algorithm, we kindly request you to cite the following paper:

• D. Entner and P. O. Hoyer. Estimating a causal order among groups of variables in linear models. In Proc. 22nd International Conference on Artificial Neural Networks (ICANN2012), pp. 83--90, Lausanne, Switzerland, 2012. [PDF]

Time series

Should you use this package for performing VAR-LiNGAM, we kindly request you to cite the following paper:

• A. Hyvärinen, K. Zhang, S. Shimizu, and P. O. Hoyer. Estimation of a structural vector autoregression model using non-Gaussianity. Journal of Machine Learning Research, 11: 1709-1731, 2010. [PDF]

Should you use this package for performing VARMA-LiNGAM, we kindly request you to cite the following paper:

• Y. Kawahara, S. Shimizu and T. Washio. Analyzing relationships among ARMA processes based on non-Gaussianity of external influences. Neurocomputing, 74(12-13): 2212-2221, 2011. [PDF]

Multiple datasets

Should you use this package for performing DirectLiNGAM for multiple groups, we kindly request you to cite the following paper:

• S. Shimizu. Joint estimation of linear non-Gaussian acyclic models. Neurocomputing, 81: 104-107, 2012. [PDF]

Should you use this package for performing LiNGAM for longitudinal data, we kindly request you to cite the following paper:

• K. Kadowaki, S. Shimizu, and T. Washio. Estimation of causal structures in longitudinal data using non-Gaussianity. In Proc. 23rd IEEE International Workshop on Machine Learning for Signal Processing (MLSP2013), pp. 1--6, Southampton, United Kingdom, 2013. [PDF]

Latent confounders and latent factors

Should you use this package for performing BottomUpParceLiNGAM with Algorithm 1 of the paper below except Step 2 for estimating causal orders, we kindly request you to cite the following paper:

• T. Tashiro, S. Shimizu, A. Hyvärinen, T. Washio. ParceLiNGAM: a causal ordering method robust against latent confounders. Neural computation, 26(1): 57-83, 2014. [PDF]

Should you use this package for performing RCD algorithm, we kindly request you to cite the following paper:

• T. N. Maeda and S. Shimizu. RCD: Repetitive causal discovery of linear non-Gaussian acyclic models with latent confounders. In Proc. 23rd International Conference on Artificial Intelligence and Statistics (AISTATS2020), Palermo, Sicily, Italy. PMLR 108:735-745, 2020. [PDF]

Should you use this package for performing LiNA algorithm, we kindly request you to cite the following paper:

• Y. Zeng, S. Shimizu, R. Cai, F. Xie, M. Yamamoto and Z. Hao. Causal Discovery with Multi-Domain LiNGAM for Latent Factors. In Proc. of the Thirtieth International Joint Conference on Artificial Intelligence (IJCAI-21), 2021: 2097--2103. [PDF]

Should you use this package for performing CAM-UV algorithm, we kindly request you to cite the following paper:

• T. N. Maeda and S. Shimizu. Causal additive models with unobserved variables. In Proc. 37th Conference on Uncertainty in Artificial Intelligence (UAI). PMLR 161:97-106, 2021. [PDF]

Should you use this package for performing GroupLiNGAM algorithm, we kindly request you to cite the following paper:

• Y. Kawahara, K. Bollen, S. Shimizu and T. Washio. GroupLiNGAM: Linear non-Gaussian acyclic models for sets of variables. Arxiv preprint arXiv:1006.5041, 2010. [PDF]

Should you use this package for performing ABIC-LiNGAM algorithm, we kindly request you to cite the following paper:

• Y. Morinishi and S. Shimizu. Differentiable causal discovery of linear non-Gaussian acyclic models under unmeasured confounding. Transactions on Machine Learning Research (TMLR), 2025. [PDF]

Causality and prediction

Should you use this package for performing estimation of intervention effects on prediction, we kindly request you to cite the following paper:

• P. Blöbaum and S. Shimizu. Estimation of interventional effects of features on prediction. In Proc. 2017 IEEE International Workshop on Machine Learning for Signal Processing (MLSP2017), pp. 1--6, Tokyo, Japan, 2017. [PDF]

Mixed data

Should you use this package for performing LiM algorithm, we kindly request you to cite the following paper:

• Y. Zeng, S. Shimizu, H. Matsui, F. Sun. Causal discovery for linear mixed data. In Proc. First Conference on Causal Learning and Reasoning (CLeaR2022). PMLR 177, pp. 994-1009, 2022. [PDF]

Missing data

Should you use this package for performing the Missingness-LiNGAM algorithm, we kindly request you to cite the following paper:

• M. Ceriscioli, S. Shimizu, and K. Mohan. Discovering Linear Non-Gaussian Models for All Categories of Missing Data (Student Abstract). The 40th Annual AAAI Conference on Artificial Intelligence (AAAI-26) Student Abstract and Poster Program, 2026. [PDF]