Basic linear models
Basic linear models with no latent confounders
(acyclic models, time series, cyclic models)
(acyclic models, time series, cyclic models)
Acyclic models
Model
NEW P. Misiakos, V. Mihal, M. Püschel. Learning Signals and Graphs from Time-Series Graph Data with Few Causes. In Proc. ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2024.
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[pdf] [TETRAD IV] [Google scholar]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(Oct): 2003--2030, 2006.
[pdf] [erratum] [Matlab/Octave code] [Google scholar]
R code by Patrik O. Hoyer and Antti Hyttinen
R code by Doris Entner
R package: pcalg by Kalisch et al.
Python code
Also implemented in TETRAD IV.S. Shimizu, A. Hyvärinen, Y. Kano and P. O. Hoyer. Discovery of non-gaussian linear causal models using ICA. In Proc. 21st Conf. on Uncertainty in Artificial Intelligence (UAI2005), pp. 525-533, Edinburgh, Scotland, 2005.
[pdf] [Google scholar]Y. Dodge and V. Rousson. On asymmetric properties of the correlation coefficient in the regression setting.
The American Statistician, 55(1): 51--54, 2001.
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[pdf] [Google scholar]
Estimation
NEW A. Shojaie, W. Chen. Learning Directed Acyclic Graphs From Partial Orderings. arXiv preprint arXiv:2403.14125, 2024.
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[pdf] [Google schlar]A. Zhang, F. Liu, W. Ma, Z. Cai, X. Wang, T.-s. Chua. Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting. arXiv:2303.03187, 2023.
[pdf] [Google schlar]I. Ng, B. Huang, K. Zhang. Structure Learning with Continuous Optimization: A Sober Look and Beyond. arXiv:2304.02146, 2023.
[pdf] [Google schlar]C. Deidda, S. Engelke, C. De Michele. Asymmetric dependence in hydrological extremes. Journal of Statistical Computation and Simulation, 2023.
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[pdf] [Google schlar]G. Ruiz, O. Madrid-Padilla, Q. Zhou. Sequential Learning of the Topological Ordering for the Linear Non-Gaussian Acyclic Model with Parametric Noise. arXiv:2202.01748, 2022.
[pdf] [Google schlar]S. Park and G. Park. Robust estimation of Gaussian linear structural equation models with equal error variances. Journal of the Korean Statistical Society, xx(x): xx-xx, 2022.
[pdf] [Google schlar]S. Xu, A. Marx, O. Mian, J. Vreeken. Causal Inference with Heteroscedastic Noise Models. In Proc. AAAI Workshop on Information Theoretic Causal Inference and Discovery (ITCI'22), 2022.
[pdf] [Google schlar]X. Chen, H. Sun, C. Ellington, E. Xing, L. Song. Multi-task Learning of Order-Consistent Causal Graphs. In Proc. 35th Conference on Neural Information Processing Systems (NeurIPS 2021) (NeurIPS 2021), 2021.
[pdf] [Google schlar]R. Zhao, X. He, J. Wang. Learning linear non-Gaussian directed acyclic graph with diverging number of nodes. arXiv:2111.00740, 2021.
[pdf] [Google schlar]H. Kawaguchi. Application of quantum computing to a linear non-Gaussian acyclic model for novel medical knowledge discovery. arXiv preprint arXiv:2110.04485, 2021.
[pdf] [Google schlar]A. Shahbazinia, S. Salehkaleybar, M. Hashemi. ParaLiNGAM: Parallel Causal Structure Learning for Linear non-Gaussian Acyclic Models. Arxiv preprint arXiv:2109.13993, 2021.
[pdf] [Google schlar]K. Harada, H. Fujisawa. Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery. Neurocomputing, xx(x): xx-xx, 2021.
[pdf] [Google scholar]G. Park, S. Moon, J.-J. Jeon. Learning a High-dimensional Linear Structural Equation Model via l1-Regularized Regression. Journal of Machine Learning Research, xx(x): xx-xx, 2021.
[pdf] [Google scholar]M. Kaiser, M. Sipos. Unsuitability of NOTEARS for Causal Graph Discovery. Arxiv preprint arXiv:2104.05441, 2021.
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[pdf] [Google schlar]K. Harada, and H. Fujiasawa. Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis. arXiv:2009.03077, 2020.
[pdf] [Google schlar]G. Park, and Y. Kim. Learning high-dimensional Gaussian linear structural equation models with heterogeneous error variances. Computational Statistics & Data Analysis, xx(x): xx-xx, 2020.
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[pdf] [code] [Google scholar]G Mai, Y Hong, P Chen, K Chen, H Huang, G Zheng. Distinguish Markov Equivalence Classes from Large-Scale Linear Non-Gaussian Data. IEEE Access, xx(x): xx-xx, 2020.
[pdf] [Google scholar]C. Yan and S. Zhou. Effective and Scalable Causal Partitioning Based on Low-order Conditional Independent Tests. Neurocomputing, xx(x): xx-xx, 2020.
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[pdf] [Google scholar]F. Xie, R. Cai, Y. Zeng, Z. Hao. Causal Discovery of Linear Non-Gaussian Acyclic Model with Small Samples. In Proc. 9th Intelligence Science and Big Data Engineering. Big Data and Machine Learning (IScIDE 2019), pp. 381-393, 2019.
[pdf] [Google scholar]H. Zhang, S. Zhou, J. Guan, J. L. Huan. Measuring Conditional Independence by Independent Residuals for Causal Discovery. ACM Transactions on Intelligent Systems and Technology (TIST) , 10(5): xx-xx, 2019.
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[pdf] [Google scholar]W. Wiedermann and X Li. Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS. Behavior Research Methods, pp. xx-xx, 2018.
[pdf] [Google scholar]R. Cai, J. Qiao, Z. Zhang, and Z. Hao. SELF: Structural equational likelihood framework for causal discovery. In Proc. 32nd AAAI Conference on Artificial Intelligence (AAAI2018), pp. xx-xx, 2018.
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[pdf] [Google scholar]W. Wiedermann and M. Hagmann. Asymmetric properties of the Pearson correlation coefficient: Correlation as the negative association between linear regression residuals. Communications in Statistics - Theory and Methods, xx(xx): xx--xx, 2015. In press.
[pdf] [Google scholar]W. Wiedermann and A. von Eye. Direction-dependence analysis: A confirmatory approach for testing directional theories. International Journal of Behavioral Development, xx(xx): xx--xx, 2015. In press.
[pdf] [Google scholar]F. Thoemmes. Empirical evaluation of directional-dependence tests. International Journal of Behavioral Development, xx(xx): xx--xx, 2015. In press.
[pdf] [Google scholar]P-L. Loh and P. Bühlmann. High-dimensional learning of linear causal networks via inverse covariance estimation. Journal of Machine Learning Research, 15(Oct):3065−3105, 2014.
[pdf] [Google scholar]W. Wiedermann, M. Hagmann and A. von Eye. Significance tests to determine the direction of effects in linear regression models. British Journal of Mathematical and Statistical Psychology, 68(1): 116--141, 2015.
[pdf] [Google scholar]D. Feng, F. Chen and W. Xu. Learning linear non-Gaussian networks: A new view from matrix identification. Journal of Experimental & Theoretical Artificial Intelligence, 25(2): 251--271, 2013.
[pdf] [Google scholar]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] [Matlab code] [Google scholar]A. Hyvärinen. Pairwise measures of causal direction in linear non-Gaussian acyclic models. In JMLR Workshop and Conference Proceedings (Proc. 2nd Asian Conference on Machine Learning, ACML2010), 13: 1-16, 2010.
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[pdf] [Google scholar]R. Henao and O. Winther. Sparse linear identifiable multivariate modeling. Journal of Machine Learning Research, 12(Mar): 863--905, 2011.
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[pdf] [Google scholar]P. O. Hoyer and A. Hyttinen. Bayesian discovery of linear acyclic causal models. In Proc. 25th Conf. on Uncertainty in Artificial Intelligence (UAI2009), pp. 240-248, Montreal, Canada, 2009.
[pdf] [code] [Google scholar]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] [Matlab/Python code] [R code by Genta Kikuchi] [Double-pendulum data] [General social survey] [Google scholar]T. Inazumi, S. Shimizu and T. Washio. Use of prior knowledge in a non-Gaussian method for learning linear structural equation models. In Proc. 9th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA2010), Saint-Malo, France, pp.221--228, 2010.
[pdf] [Matlab code] [Google scholar]Y. Sogawa, S. Shimizu, Y. Kawahara and T. Washio. An experimental comparison of linear non-Gaussian causal discovery methods and their variants. In Proc. Int. Joint Conference on Neural Networks (IJCNN2010), pp. 768--775, Barcelona, Spain, 2010.
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[pdf] [notes] [erratum] [Matlab code] [Google scholar]Y. Sogawa, S. Shimizu, T. Shimamura, A. Hyvärinen, T. Washio and S. Imoto. Estimating exogenous variables in data with more variables than observations. Neural Networks, 24(8): 875-880, 2011 (Selected papers from ICANN2010).
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[pdf] [Google scholar]
Time series
Structural vector autoregressive models
A. Bagheri, M. Pasande, K. Bello, A. Akhondi-Asl, B. N. Araabi. Bayesian Dynamic DAG Learning: Application in Discovering Dynamic Effective Connectome of Brain. Arxiv preprint arXiv:22306.08765, 2022.
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[pdf] [Google scholar]G. Bormetti, F. Corsi. A Lucas Critique Compliant SVAR model with Observation-driven Time-varying Parameters. Arxiv preprint arXiv:2107.05263, 2021.
[pdf] [Google scholar]M. Lanne, J. Luoto. GMM Estimation of Non-Gaussian Structural Vector Autoregression. Journal of Business & Economic Statistics, 39(1): 69-81, 2021.
[pdf] [Google scholar]S. M. Zema. Non-Normal Identification for Price Discovery in High-Frequency Financial Markets. LEM Working Paper Series, ISSN(ONLINE) 2284-0400, 2020.
[pdf] [Google scholar]C. Velasco. Identification and estimation of Structural VARMA models using higher order dynamics. Arxiv preprint arXiv:2009.04428, 2020.
[pdf] [Google scholar]P. Xie, J. Ye, J. Wang. Volatility Estimation of Multivariate ARMA-GARCH Model. Journal of Harbin Institute of Technology (New Series), 27(1): 36-43, 2020.
[pdf] [Google scholar]R. Pamfil, N. Sriwattanaworachai, S. Desai, P. Pilgerstorfer, P. Beaumont, K. Georgatzis, B. Aragam. DYNOTEARS: Structure Learning from Time-Series Data. JMLR Workshop and Conference Proceedings, AISTATS 2020 (Proc. 23th International Conference on Artificial Intelligence and Statistics), x: xx-xx, 2020.
[pdf] [Google scholar]B. Huang, K. Zhang, J. Zhang, J. Ramsey, B. Schölkopf. Causal Discovery and Hidden Driving Force Estimation from Nonstationary/Heterogeneous Data. Arxiv preprint arXiv:1903.01672, 2019.
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[pdf] [Google scholar]S. Bauer, B. Schölkopf, and J. Peters. The arrow of time in multivariate time series. Arxiv preprint arXiv:1603.00784, 2016.
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[pdf] [Google scholar]W. Wiedermann and A. von Eye. Directional dependence in the analysis of single subjects. Journal of Person-Oriented Research, 2(1-2): 20-33, 2016.
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[pdf] [Google scholar]M. Lanne, M. Meitz, and P. Saikkon. Identification and estimation of non-Gaussian structural vector autoregressions. CREATES Research Paper 2015-1, 2015.
[pdf] [Google scholar]B. Huang, K. Zhang, and B. Schölkopf. Identification of time-dependent causal model: a Gaussian process treatment. In Proc. 24th International Joint Conference on Artificial Intelligence (IJCAI2015), pp. xx-xx, Buenos Aires, Argentina, 2015.
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[pdf] [Google scholar]Z. Chen, K. Zhang and L. Chan. Causal discovery with scale-mixture model for spatiotemporal variance dependencies. In Advances in Neural Information Processing Systems 25 (NIPS2012), pp. xx-xx, 2012.
[pdf] [Google scholar]W. Gao and H. Yang. Identifying structural VAR model with latent variables using overcomplete ICA. Far East Journal of Theoretical Statistics, 40(1): 31-44, 2012.
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[pdf] [Related code] [Python code by T. Ikeuchi and G. Haraoka] [real data] [Google scholar]M. Lanne and H. Lütkepohl. Structural vector autoregressions with nonnormal residuals. Journal of Business & Economic Statistics, 28(1): 159-168, 2010.
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[pdf] [Google scholar]
R code by Doris Entner
Matlab code by Luca Faes
Python code by T. Ikeuchi and G. HaraokaA. Hyvärinen, S. Shimizu and P. O. Hoyer. Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-Gaussianity. In Proc. Int. Conf. on Machine Learning (ICML2008), pp. 424-431, Helsinki, Finland, 2008.
[pdf] [videolecture] [Google scholar]
Others
K. Du, Y. Xiang . Causal Inference Using Linear Time-Varying Filters with Additive Noise. Arxiv preprint arXiv:2012.13025, 2020.
[pdf] [Google scholar]D. Malinsky, and P. Spirtes. Causal Structure Learning from Multivariate Time Series in Settings with Unmeasured Confounding. In Proc. 2018 ACM SIGKDD Workshop on causal discovery (CD2018), pp. xx-xx, London, UK, 2015.
[pdf] [Google scholar]P. Geiger, K. Zhang, M. Gong, D. Janzing, and B. Schölkopf. Causal inference by identification of vector autoregressive processes with hidden components. In Proc. 32nd International Conference on Machine Learning (ICML2015), pp. xx-xx, Lille, France, 2015.
[pdf] [Google scholar]P. Morales-Mombiela, D. Hernández-Lobato and A. Suárez. Statistical tests for the detection of the arrow of time in vector autoregressive models. In Proc. 23rd International Joint Conference on Artificial Intelligence (IJCAI2013), pp. 1544-1550, Beijing, China, 2013.
[pdf] [Google scholar]J. M. Hernández-Lobato, P. Morales-Mombiela and A. Suárez. Gaussianity measures for detecting the direction of causal time series. In Proc. 22nd International Joint Conference on Artificial Intelligence (IJCAI2011), pp. 1318-1323, Barcelona, Catalonia (Spain), 2011.
[pdf] [Google scholar]R. Henao and O. Winther. Sparse linear identifiable multivariate modeling. Journal of Machine Learning Research, 12(Mar): 863--905, 2011.
[pdf] [code] [Google scholar]D. Janzing. On the entropy production of time series with unidirectional linearity. Journal of Statistical Physics, 138(4-5): 767-779, 2010.
[pdf] [Google scholar]J. Peters, D. Janzing, A. Gretton and B. Schölkopf. Detecting the direction of causal time series. In Proc. 26th Int. Conf. on Machine Learning (ICML2009), pp. 801-808, Montreal, Canada, 2009.
[pdf] [code] [Google scholar]
Cyclic models
NEW H. Dai, I. Ng, Y. Zheng, Z. Gao, K. Zhang. Local Causal Discovery with Linear non-Gaussian Cyclic Models. arXiv:2403.14843, 2024.
[pdf] [Google scholar]S. Roy, R. K. W. Wong, Y. Ni. Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data. arXiv:2310.20537, 2023.
[pdf] [Google scholar]M. Drton, B. Hollering, J. Wu. Identifiability of Homoscedastic Linear Structural Equation Models using Algebraic Matroids. arXiv:2308.01821, 2013.
[pdf] [Google scholar]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] [Matlab code] [Google scholar]J. Hirayama and A. Hyvärinen. Structural equations and divisive normalization for energy-dependent component analysis. In Advances in Neural Information Processing Systems 24 (NIPS2011), pp. xx-xx, 2011.
[pdf] [Google scholar]G. Lacerda, P. Spirtes, J. Ramsey and P. O. Hoyer. Discovering cyclic causal models by independent components analysis. In Proc. 24th Conf. on Uncertainty in Artificial Intelligence (UAI2008), pp. 366-374, Helsinki, Finland, 2008.
[pdf] [videolecture] [TETRAD IV] [Google scholar] [Code by Genya Haraoka]