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Causal discovery and machine learning
Causal discovery and machine learning
NEW H. Yokoyama, R. Shingaki, K. Nishino, S. Shimizu, T. Pham. Causal-discovery-based root-cause analysis and its application in time-series prediction error diagnosis. Arxiv preprint arXiv: 2411.06990, 2024. Accepted in Proc. IJCNN2025.
[pdf] [Google scholar]M. Takayama, T. Okuda, T. Pham, T. Ikenoue, S. Fukuma, S. Shimizu, A. Sannai. Integrating large language models in causal discovery: a statistical causal approach. Arxiv preprint arXiv:2402.01454, 2024. Accepted in TMLR.
[pdf] [Google scholar]D. Takahashi, S. Shimizu, and T. Tanaka. Counterfactual explanations of black-box machine learning models using causal discovery with applications to credit rating. In Proc. Int. Joint Conf. on Neural Networks (IJCNN2024), part of the 2024 IEEE World Congress on Computational Intelligence (WCCI2024), pages 1--8, Yokohama, Japan, 2024.
[pdf] [Google scholar]K. Kiritoshi, T. Izumitani, K. Koyama, T. Okawachi, K. Asahara, and S. Shimizu. Estimating individual-level optimal causal interventions combining causal models and machine learning models. In Proc. KDD'21 Workshop on Causal Discovery, PMLR 150:55-77, 2021.
[pdf] [Google scholar]
[Proposes a method for estimating individual-level optimal causal intervention by combining causal discovery and machine learning.]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] [Google scholar]
A short introduction
Python code
[Proposes a new framework to understand the prediction mechanisms of predictive models based on causality.]
Case studies of causal discovery
Case studies of causal discovery
Y. Jiang and S. Shimizu. Does Financial Literacy Impact Investment Participation and Retirement Planning in Japan?. arXiv:2405.01078, 2024.
[pdf] [Google scholar]Y. Jiang and S. Shimizu. Linkages among the foreign exchange, stock, and bond markets in Japan and the United States. In Proc. Causal Analysis Workshop 2023 (CAWS2023), PMLR 223:1-19, 2023.
[pdf] [Google scholar]高山正行, 小柴等, 前田高志ニコラス, 三内顕義, 清水昌平, 星野利彦. 博士課程進学率に関する因果モデルの構築. Jxiv, JST プレプリントサーバ, 2022.
[pdf] [Google scholar]
Causal discovery software
Causal discovery software
Y. Zheng, B. Huang, W. Chen, J. Ramsey, M. Gong, R. Cai, S. Shimizu, P. Spirtes, K. Zhang. Causal-learn: Causal discovery in Python. Journal of Machine Learning Research, 25(60):1−8, 2024.
[A Python package for performing causal discovery methods including conditonal-independence-based methods and LiNGAM methods.]
[pdf] [github] [Google scholar]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] [Google scholar]
Python package
[A Python package for performing causal discovery analysis based on LiNGAM approach.]
[LiNGAM Python package: Tutorial slides]
[LiNGAM Pythonパッケージでできること: 紹介スライド]
Causal discovery: LiNGAM
Causal discovery: LiNGAM
LiNGAM homepage
Links to LiNGAM-related papers
Reviews and tutorials
T. N. Maeda, Y. Zeng, and S. Shimizu. Causal discovery with hidden variables based on non-Gaussianity and non-linearity. In Dependent Data in Social Sciecnes Research - Forms, Issues and Methods of Analysis (2nd edition), pages 181–205. Springer, 2024.
[pdf] [Google scholar]S. Shimizu. Statistical causal discovery: LiNGAM approach. SpringerBriefs in Statistics. Springer Tokyo, 2022.
[pdf] [Google scholar]S. Shimizu and P. Blöbaum. Recent advances in semi-parametric methods for causal discovery. In Direction Dependence in Statistical Models: Methods of Analysis (W. Wiedermann, D. Kim, E. Sungur, and A. von Eye, eds.), pages xx–xx. Wiley, 2020.
[pdf] [Google scholar]S. Shimizu. LiNGAM: Non-Gaussian methods for estimating causal structures. Behaviormetrika, 41(1): 65--98, 2014.
[pdf] [Google scholar]S. Shimizu. Non-Gaussian Methods for Learning Linear Structural Equation Models: Part I. The 26th Conference on Uncertainty in Artificial Intelligence (UAI2010), Catalina Island, California, USA , 2010. Tutorial
[slides] [references]
Basic models with no hidden variables
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, pages 994-1009, 2022.
[pdf] [Google scholar]
Python code
[Proposes an approach for inferring causal structure from mixed continuous and discrete data combining LiNGAM and logistic-type model.]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] [Google scholar]
Videolecture
R code by Doris Entner
Matlab code by Luca Faes
Python code
[Shows how LiNGAM and autoregressive models are combined to estimate a structural vector autoregression model for time series data.]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] [Python code] [Google scholar]
[Considers learning causal structures in longitudinal data that collects multiple samples over a period of time.]S. Shimizu. Joint estimation of linear non-Gaussian acyclic models. Neurocomputing, 81: 104-107, 2012.
[pdf] [Google scholar]
Python code
[Proposes a framework to perform LiNGAM analysis on heterogenous datasets.]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] [Google scholar]
Python code
R code by Genta Kikuchi
[Proposes a new estimation algorithm for LiNGAM. The new estimation method called DirectLiNGAM requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, i.e., if all the model assumptions are met and the sample size is infinite.]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] [Matlab/Octave code] [Google scholar]
A short introduction
R code by Patrik O. Hoyer and Antti Hyttinen
R code by Doris Entner
R package: pcalg by Kalisch et al.
Python code
TETRAD IV
[Proposes a novel identifiable model (LiNGAM) for causal discovery and an ICA-based estimation algorithm to learn the model. Original article introducing LiNGAM.]
Hidden variable models
NEW Y. Morinishi and S. Shimizu. Differentiable causal discovery of linear non-Gaussian acyclic models under unmeasured confounding. Arxiv preprint arXiv: 2501.12854, 2025.
[pdf] [Google scholar]
[Proposes a continuous-optimization-based estimation method for a non-Gaussian causal model with hidden common causes.]Y. Zeng, S. Shimizu, R. Cai, F. Xie, M. Yamamoto, Z. Hao. Causal discovery with multi-domain LiNGAM for latent factors. In Proc. the 30th International Joint Conference on Artificial Intelligence (IJCAI2021), pages xx-xx, Montreal-themed Virtual Reality, 2021.
[pdf] [Google scholar]
Python code
[Considers to estimate LiNGAM model for latent factors from multi-domain data.]T. N. Maeda and S. Shimizu. RCD: Repetitive causal discovery of linear non-Gaussian acyclic models with latent confounders. In JMLR Workshop and Conference Proceedings, AISTATS2020 (Proc. 23rd International Conference on Artificial Intelligence and Statistics), pages 735–745, Palermo, Sicily, Italy, 2020.
[pdf] [Google scholar]
Python code
[Proposes an extension of the LiNGAM model that allows hidden common causes.]T. Tashiro, S. Shimizu, A. Hyvärinen and T. Washio. ParceLiNGAM: A causal ordering method robust against latent confounders. Neural Computation, 26(1): 57--83, 2014.
[pdf] [Google scholar]
code
[Develops a variant of DirectLiNGAM that is robust against hidden common causes. ]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] [Google scholar]P. O. Hoyer, S. Shimizu, A. Kerminen, and M. Palviainen. Estimation of causal effects using linear non-gaussian causal models with hidden variables. International Journal of Approximate Reasoning, 49(2): 362-378, 2008.
[pdf] (7.0MB) [doi] [Matlab code] [Google scholar]
[Proposes an extension of basic LiNGAM above to cases with latent common cause variables. The new model is called Latent variable LiNGAM (LvLiNGAM). ]
Nonlinearity
NEW T. Pham, T. N. Maeda, and S. Shimizu. Causal Additive Models with Unobserved Causal Paths and Backdoor Paths. Arxiv preprint arXiv: 2502.07646, 2025.
[pdf] [Google scholar]
[Shows that resolving the causal direction in the presence of hidden common causes is feasible in certain scenarios.]NEW T. N. Maeda and S. Shimizu. Use of prior knowledge to discover causal additive models with unobserved variables and its application to time series data. Behaviormetrika, xx(xx): xx-xx, 2024. In press.
[pdf] [Google scholar]
[Extends that CAM-UV so that it can incorporate prior knowlede and handle time series data.]G. Kikuchi and S. Shimizu. Structure Learning for Groups of Variables in Nonlinear Time-Series Data with Location-Scale Noise. In Proc. Causal Analysis Workshop 2023 (CAWS2023), PMLR 223:20-39, 2023.
[pdf] [Google scholar]
[Proposes a structure-learning algorithm for nonlinear time-series data with location-scale noise.]D. Fujiwara, K. Koyama, K. Kiritoshi, T. Okawachi, T. Izumitani, and S. Shimizu. Causal Discovery for Non-stationary Non-linear Time Series Data Using Just-In-Time Modeling. In Proc. 2nd Conference on Causal Learning and Reasoning, PMLR 213: 880-894, 2023.
[pdf] [Google scholar]
[Proposes a causal discovery method JIT-LiNGAM, based on the Linear Non-Gaussian Acyclic Model (LiNGAM) and the Just-In-Time (JIT) framework to approximate an inherently globally non-linear model with local linear models.]K. Uemura, T. Takagi, T. Kambayashi, H. Yoshida, and S. Shimizu. A Multivariate Causal Discovery based on Post-Nonlinear Model. In Proc. First Conference on Causal Learning and Reasoning (CLeaR2022), PMLR 177, pages 826-839, 2022.
[pdf] [Google scholar]
Python code
[Proposes a multivariate estimation method for post-nonlinear causal model using an autoenconding structure.]T. N. Maeda and S. Shimizu. Causal additive models with unobserved variables. In Proc. 37th Conf. on Uncertainty in Artificial Intelligence (UAI2021), pages xx–xx, Online, 2021.
[pdf] [Google scholar]
Python code
Python code in causal-learn
[Proposes an additive nonlinear model that allows unobserved common causes and unobserved intermediate variables.]
Statistical reliability
Y. Komatsu, S. Shimizu, and H. Shimodaira. Assessing statistical reliability of LiNGAM via multiscale bootstrap. In Proc. 20th International Conference on Artificial Neural Networks (ICANN2010), pp.309--314, Thessaloniki, Greece, 2010.
[pdf] [doi] [Google scholar]
Related code: R code for multiscale bootstrap
[Proposes a method to evaluate statistical reliability of causal orderings estimated by LiNGAM.]
Model fit
S. Shimizu and Y. Kano. Use of non-normality in structural equation modeling: Application to direction of causation. Journal of Statistical Planning and Inference, 138: 3483--3491, 2008.
[pdf] [Google scholar]
[Proposes a test statistics to evaluate model fit using higher-order moments.]
Causal inference: misc.
Causal inference: misc.
NEW J. Long, Y. Yang, S. Shimizu, T. Pham, and K.-A. Do. Causal models and prediction in cell line perturbation experiments. BMC Bioinformatics, 26: Article number 4, 2025.
[pdf] [Google scholar]T. Pham, S. Shimizu, H. Hino, T. Le. Scalable counterfactual distribution estimation in multivariate causal models. In Proc. Third Conference on Causal Learning and Reasoning (CLeaR2024), PMLR 236:1118-1140, 2024.
[pdf] [Google scholar]D. Fujiwara, K. Koyama, K. Kiritoshi, T. Okawachi, T. Izumitani, and S. Shimizu. Prospects of continual causality for industrial applications. In Proc. First AAAI Bridge Program on Continual Causality, PMLR 208:18-24, 2023.
[pdf] [Google scholar]Y. Zeng, Z. Hao, R. Cai, F. Xie, L. Huang, S. Shimizu. Nonlinear causal discovery for high-dimensional deterministic data. IEEE Transactions on Neural Networks and Learning Systems, xx: xx--xx, 2021.
[pdf] [Google scholar]
[Proposes a nonlinear method for estimating the causal structure of variables in deterministic cases.]P. Blöbaum, D. Janzing, T. Washio, S. Shimizu, B. Schölkopf. Cause-effect inference by comparing regression errors. In Proc. International Conference on Artificial Intelligence and Statistics (AISTATS2018), PMLR 84:900-909, 2018.
[pdf] [Google scholar]
[Proposes a nonlinear method for estimating the causal direction of two variables comparing the least-squares errors. ]R. Silva and S. Shimizu. Learning instrumental variables with structural and non-Gaussianity assumptions. Journal of Machine Learning Research, 18: 1--49, 2017.
[pdf] [Google scholar]
[Proposes a method for learning instrumental variables based on non-Gaussianity.]
Machine learning: misc.
Machine learning: misc.
K. Honjo, X. Zhou, S. Shimizu. CNN-GRU based deep learning model for demand forecast in retail industry. In Proc. International Joint Conference on Neural Networks (IJCNN2022), part of the 2022 IEEE World Congress on Computational Intelligence (WCCI2022)}, 1-8, 2022.
[pdf] [Google scholar]
[Constructs a deep learning model for demand forecasting in the retail industry.]
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