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LiNGAM - Discovery of non-gaussian linear causal models\r\n\r\n[![License](https://img.shields.io/badge/license-MIT-blue.svg)](https://github.com/cdt15/lingam/blob/master/LICENSE)\r\n[![Read the Docs](https://readthedocs.org/projects/lingam/badge/?version=latest)](https://lingam.readthedocs.io/)\r\n\r\nLiNGAM is a new method for estimating structural equation models or linear Bayesian networks. It is based on using the non-Gaussianity of the data.\r\n\r\n* [The LiNGAM Project](https://sites.google.com/view/sshimizu06/lingam)\r\n\r\n## Requirements\r\n\r\n* Python3\r\n* numpy\r\n* scipy\r\n* scikit-learn\r\n* graphviz\r\n* statsmodels\r\n* networkx\r\n* pandas\r\n* itertools\r\n* semopy\r\n* autograd\r\n\r\n\r\n## Installation\r\n\r\nTo install lingam package, use `pip` as follows:\r\n\r\n```sh\r\npip install lingam\r\n```\r\n\r\n## Usage\r\n\r\n```python\r\nimport numpy as np\r\nimport pandas as pd\r\nimport lingam\r\n\r\n# To run causal discovery, we create a DirectLiNGAM object and call the fit method.\r\nmodel = lingam.DirectLiNGAM()\r\nmodel.fit(X)\r\n\r\n# Using the causal_order_ properties,\r\n# we can see the causal ordering as a result of the causal discovery.\r\nprint(model.causal_order_)\r\n\r\n# Also, using the adjacency_matrix_ properties,\r\n# we can see the adjacency matrix as a result of the causal discovery.\r\nprint(model.adjacency_matrix_)\r\n```\r\n\r\n## Documentation\r\n\r\n[Tutorial and API reference](https://lingam.readthedocs.io/)\r\n\r\n[Tutorial slides](https://speakerdeck.com/sshimizu2006/lingam-python-package)\r\n\r\n## Examples\r\n\r\nWe provide several examples of running the LiNGAM algorithm in Jupyter Notebook.\r\n [lingam/examples](./examples)\r\n\r\n## License\r\n\r\nThis project is licensed under the terms of the [MIT license](./LICENSE).\r\n\r\n## Contribution\r\n\r\nFor guidelines how to contribute to lingam package, take a look at [CONTRIBUTING.md](./CONTRIBUTING.md).\r\n\r\n## References\r\n\r\n### Package\r\n\r\nIf you find our package useful, please cite the following paper:\r\n\r\n* 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]](https://jmlr.org/papers/v24/21-0321.html)\r\n\r\n\r\n### Basic DAG model\r\n\r\nShould you use this package for performing **ICA-based LiNGAM algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](http://www.jmlr.org/papers/volume7/shimizu06a/shimizu06a.pdf)\r\n\r\nShould you use this package for performing **DirectLiNGAM algorithm**, we kindly request you to cite the following two papers:\r\n\r\n* 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]](http://www.jmlr.org/papers/volume12/shimizu11a/shimizu11a.pdf)\r\n* 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]](http://www.jmlr.org/papers/volume14/hyvarinen13a/hyvarinen13a.pdf)\r\n\r\nShould you use this package for performing **RESIT algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](http://www.jmlr.org/papers/volume15/peters14a/peters14a.pdf)\r\n\r\nShould you use this package for performing **GroupDirectLiNGAM algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://link.springer.com/chapter/10.1007/978-3-642-33266-1_11)\r\n\r\n\r\n### Time series\r\n\r\nShould you use this package for performing **VAR-LiNGAM**, we kindly request you to cite the following paper:\r\n\r\n* 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]](http://www.jmlr.org/papers/volume11/hyvarinen10a/hyvarinen10a.pdf)\r\n\r\nShould you use this package for performing **VARMA-LiNGAM**, we kindly request you to cite the following paper:\r\n\r\n* 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]](http://dx.doi.org/10.1016/j.neucom.2011.02.008)\r\n\r\n\r\n### Multiple datasets\r\n\r\nShould you use this package for performing **DirectLiNGAM for multiple groups**, we kindly request you to cite the following paper:\r\n\r\n* S. Shimizu. **Joint estimation of linear non-Gaussian acyclic models**. *Neurocomputing*, 81: 104-107, 2012. [[PDF]](http://dx.doi.org/10.1016/j.neucom.2011.11.005)\r\n\r\nShould you use this package for performing **LiNGAM for longitudinal data**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://doi.org/10.1109/MLSP.2013.6661912)\r\n\r\n\r\n### Latent confounders and latent factors\r\n\r\nShould 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:\r\n\r\n* 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]](https://ieeexplore.ieee.org/abstract/document/6797648)\r\n\r\nShould you use this package for performing **RCD algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](http://proceedings.mlr.press/v108/maeda20a.html)\r\n\r\nShould you use this package for performing **LiNA algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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](https://www.ijcai.org/proceedings/2021/289)]\r\n\r\nShould you use this package for performing **CAM-UV algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://proceedings.mlr.press/v161/maeda21a.html)\r\n\r\nShould you use this package for performing **GroupLiNGAM algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://arxiv.org/abs/1006.5041)\r\n\r\nShould you use this package for performing **ABIC-LiNGAM algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://openreview.net/forum?id=HR7MFlW73I)\r\n\r\n\r\n### Causality and prediction\r\n\r\nShould you use this package for performing **estimation of intervention effects on prediction**, we kindly request you to cite the following paper:\r\n\r\n* 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]](https://doi.org/10.1109/MLSP.2017.8168175)\r\n\r\n### Mixed data\r\n\r\nShould you use this package for performing **LiM algorithm**, we kindly request you to cite the following paper:\r\n\r\n* 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. 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