Causality and prediction

  • NEW 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.]

Causal discovery: LiNGAM

LiNGAM homepage
Links to LiNGAM-related papers

Reviews and tutorials

  • 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

  • C. Li and S. Shimizu. Combining linear non-Gaussian acyclic model with logistic regression model for estimating causal structure from mixed continuous and discrete data. Arxiv preprint arXiv:1802.05889, 2018.
    [pdf] [Google scholar]
    [Proposes an approach for inferring causal structure from mixed continuous and discrete data combining LiNGAM and logistic regression 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]
    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. This is based on ICML2008 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] [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] [erratum] [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
    [Proposes a novel identifiable model (LiNGAM) for causal discovery and an ICA-based estimation algorithm to learn the model. Original article introducing LiNGAM. This is based on UAI2005 paper.]

Hidden variable models

  • NEW 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]
    [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]

  • 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]
    [Develops a variant of DirectLiNGAM that is robust against hidden common causes. This is based on ICANN2012 paper.]

  • S. Shimizu and K. Bollen. Bayesian estimation of causal direction in acyclic structural equation models with individual-specific confounder variables and non-Gaussian distributions. Journal of Machine Learning Research, 15: 2629-2652, 2014.
    [pdf] [Google scholar]
    A short introduction
    Python code
    [Considers the problem of estimating the causal direction of two observed variables in the presence of hidden common causes. Develops a new approach based on a linear non-Gaussian acyclic structural equation model (LiNGAM) and a linear mixed model. The new approach does not require to specify the number of hidden common causes.]

  • 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). This is based on PGM2006 paper.]


  • NEW 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]

  • K. Uemura and S. Shimizu. Estimation of post-nonlinear causal models using autoencoding structure. In Proc. 45th International Conference on Acoustics, Speech, and Signal Processing (ICASSP2020), pages 3312-3316, Barcelona, Spain, 2020.
    [pdf] [Google scholar]
    [Proposes an estimation method for post-nonlinear causal model using an autoenconding structure.]

Statistical reliability

  • K. Thamvitayakul, S. Shimizu, T. Ueno, T. Washio and T. Tashiro. Bootstrap confidence intervals in DirectLiNGAM. In Proc. 2012 IEEE 12th International Conference on Data Mining Workshops (ICDMW2012), pp.659--668, Brussels, Belgium, 2012.
    [pdf] [erratum] [Google scholar]
    [Considers to compute Bootstrap confidence intervals in LiNGAM.]

  • 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.

  • P. Blöbaum, D. Janzing, T. Washio, S. Shimizu, B. Schölkopf. Analysis of cause-effect inference by comparing regression errors. PeerJ Computer Science 5:e169, 2019.
    [pdf] [Google scholar]
    [Proposes a nonlinear method for estimating the causal direction of two variables comparing the least-squares errors. This is based on AISTATS2018 paper. ]

  • 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.]