Basic linear models

Basic linear models with no latent confounders
(acyclic models, time series, cyclic models)

Acyclic models

Model

  • C. Améndola, M. Drton, A. Grosdos, R. Homs, E. Robeva. Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models. Arxiv preprint arXiv:2112.10875, 2021.
    [pdf] [Google scholar]

  • G. Park. Identifiability of Additive Noise Models Using Conditional Variances. Journal of Machine Learning Research, 21: 1--34, 2020.
    [pdf] [Google scholar]

  • G. Park and Y. Kim. Identifiability of Gaussian Structural Equation Models with Homogeneous and Heterogeneous Error Variances. Journal of the Korean Statistical Society, xx(xx): xx--xx, 2020.
    [pdf] [Google scholar]

  • S. Yu, M. Drton, A. Shojaie. Directed Graphical Models and Causal Discovery for Zero-Inflated Data. Arxiv preprint arXiv:2004.04150, 2020.
    [pdf] [Google schlar]

  • N. Gnecco, N. Meinshausen, J. Peters, S. Engelke. Causal discovery in heavy-tailed models. Arxiv preprint arXiv:1908.05097, 2019.
    [pdf] [Google scholar]

  • W. Wiedermann and A. von Eye. Testing the causal direction of mediation effects in randomized intervention studies. Prevention Science, xx(xx): xx--xx, 2018.
    [pdf] [Google scholar]

  • A Ghoshal and J Honorio. Learning identifiable Gaussian Bayesian networks in polynomial time and sample complexity. Arxiv preprint arXiv:1703.01196, 2017.
    [pdf] [Google scholar]

  • A. Ghoshal and J. Honorio. Learning linear structural equation models in polynomial time and sample complexity. Arxiv preprint arXiv:1707.04673, 2017.
    [pdf] [Google scholar]

  • W. Wiedermann and A. von Eye. Direction of effects in mediation analysis. Psychological Methods, 20(2): 221--244, 2015.
    [pdf] [Google scholar]

  • W. Wiedermann and A. von Eye. Direction of effects in multiple linear regression models. Multivariate Behavioral Research, 50(1): 23--40, 2015.
    [pdf] [Google scholar]

  • A. Sokol, M. H. Maathuis and B. Falkeborg. Quantifying identifiability in independent component analysis. Electronic Journal of Statistics, 8: 1438--1459, 2014.
    [pdf] [Google scholar]

  • J. Peters and P. Bühlmann. Identifiability of Gaussian structural equation models with equal error variances. Biometrika, 101(1): 219--228, 2014.
    [pdf] [Google scholar]

  • 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] [code] [Google scholar]

  • P. O. Hoyer, A. Hyvärinen, R. Scheines, P. Spirtes, J. Ramsey, G. Lacerda, and S. Shimizu. Causal discovery of linear acyclic models with arbitrary distributions. In Proc. 24th Conf. on Uncertainty in Artificial Intelligence (UAI2008), pp. 282-289, Helsinki, Finland, 2008.
    [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.
    [pdf] [Google scholar]

  • Y. Dodge and V. Rousson. Direction dependence in a regression line. Communications in Statistics - Theory and Methods, 29(9-10): 1957--1972, 2000.
    [pdf] [Google scholar]

Estimation

  • NEW H. Zhang, K. Zhang, S. Zhou, J. Guan. Residual Similarity Based Conditional Independence Test and Its Application in Causal Discovery. In Proc. 36th AAAI Conference on Artificial Intelligence (AAAI2022), pp. xx-xx, 2022.
    [pdf] [Google scholar]

  • S. Dong, M. Sebag. From graphs to DAGs: a low-complexity model and a scalable algorithm. arXiv:2204.04644, 2022.
    [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.
    [pdf] [Google schlar]

  • Z. Fang, S. Zhu, J. Zhang, Y. Liu, Z. Chen, Y. He. Low Rank Directed Acyclic Graphs and Causal Structure Learning. Arxiv preprint arXiv:2006.05691, 2020.
    [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]

  • I. Ng, A. E. Ghassami, K. Zhang. On the Role of Sparsity and DAG Constraints for Learning Linear DAGs. Arxiv preprint arXiv:2006.10201, 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.
    [pdf] [Google scholar]

  • H. Zhang, S. Zhou, C. Yan, J. Guan, X. Wang, J. Zhang, and J. Huan. Learning Causal Structures Based on Divide and Conquer. IEEE Transactions on Cybernetics, xx(x): xx-xx, 2020.
    [pdf] [Google scholar]

  • Y. S. Wang and M. Drton. High-dimensional causal discovery under non-Gaussianity. Biometrika, xx(x): xx-xx, 2020.
    [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.
    [pdf] [Google scholar]

  • Y. Zeng, Z. Hao, R. Cai, F. Xie, L. Ou, R. Huang. A causal discovery algorithm based on the prior selection of leaf nodes. Neural Networks, xx(x): xx-xx, 2020.
    [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.
    [pdf] [Google scholar]

  • H. Zhang, S. Zhou, C. Yan, J. Guan, X. Wang. Recursively Learning Causal Structures Using Regression-Based Conditional Independence Test. In Proc. 33nd AAAI Conference on Artificial Intelligence (AAAI2019), pp. xx-xx, 2019.
    [pdf] [Google scholar]

  • X. Zheng, B. Aragam, P. K. Ravikumar, and E. P. Xing. DAGs with NO TEARS: Continuous Optimization for Structure Learning. In Advances in Neural Information Processing Systems 32 (NIPS2018), pp. xx-xx, 2018.
    [pdf] [Google scholar]

  • J. Yang, N. Li, N. An, Y. Chen, and G. Alterovitz. An efficient causal structure learning algorithm for linear arbitrarily distributed continuous data. The Journal of Supercomputing, pp. xx-xx, 2018.
    [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.
    [pdf] [Google scholar]

  • R. Cai, F. Xie, W. Chen, and Z. Hao. An efficient kurtosis-based causal discovery method for linear non-Gaussian acyclic data. In Proc. 2017 IEEE/ACM 25th International Symposium on Quality of Service: 208-216, 2017.
    [pdf] [Google scholar]

  • W. Wiedermann. Decisions concerning the direction of effects in linear regression models using fourth central moments. In Dependent Data in Social Sciences Research, pp. 149-169, 2015.
    [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.
    [pdf] [Google scholar]

  • Y. Dodge and I. Yadegari. On direction of dependence. Metrika, 72: 139--150, 2010.
    [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]

  • R. Henao and O. Winther. Bayesian sparse factor models and DAGs inference and comparison. In Advances in Neural Information Processing Systems 22 (NIPS2009), pp. 736-744, 2010.
    [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.
    [pdf] [Matlab code] [Google scholar]

  • S. Shimizu, A. Hyvärinen, Y. Kawahara and T. Washio. A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model. In Proc. 25th Conf. on Uncertainty in Artificial Intelligence (UAI2009), pp. 506-513, Montreal, Canada, 2009.
    [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).
    [pdf] [Matlab code] [Google scholar]

  • Y. Sogawa, S. Shimizu, A. Hyvärinen, T. Washio, T. Shimamura and S. Imoto. Discovery of exogenous variables in data with more variables than observations. In Proc. International Conference on Artificial Neural Networks (ICANN2010), pp.67-76, Thessaloniki, Greece, 2010.
    [pdf] [Matlab code] [Google scholar]

  • K. Ozaki, K. Nakamura and H. Murohashi. A multilevel model using 2nd and 3rd order moments. Proceedings of the Institute of Statistical Mathematics, 58(2): 207--221, 2010. (In Japanese)
    [pdf] [Google scholar]

  • K. Zhang, H. Peng, L. Chan and A. Hyvärinen. ICA with sparse connections: Revisited. In Proc. 8th Int. Conf. on Independent Component Analysis and Signal Separation (ICA2009), pp. 195-202, Paraty, Brazil, 2009.
    [pdf] [Google scholar]

  • A. B. Nielsen and L. K. Hansen. Structure learning by pruning in independent component analysis. Neurocomputing, 71: 2281--2290, 2008.
    [pdf] [Google scholar]

  • K. Zhang and L. Chan. ICA with sparse connections. In Proc. 7th Conf. on Intelligent Data Engineering and Automated Learning (IDEAL2006), pp. 530-537, Burgos, Spain, 2006.
    [pdf] [Google scholar]

  • 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]

Time series

Structural vector autoregressive models

  • 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.
    [pdf] [Google scholar]

  • M. Lanne, J. Luoto. Identification of Economic Shocks by Inequality Constraints in Bayesian Structural Vector Autoregression. Oxford Bulletin of Economics and Statistics, xx(xx): xx-xx, 2019.
    [pdf] [Google scholar]

  • B. Huang, K. Zhang, M. Gong, C. Glymour. Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models. In Proc. 36rd International Conference on Machine Learning (ICML2019), pp. xx-xx, Long Beach, California, 2019.
    [pdf] [Google scholar]

  • A. Tank, E. Fox, and A. Shojaie. Identifiability and estimation of structural vector autoregressive models for subsampled and mixed-frequency time series. Biometrika, 106(2), 433-452, 2019.
    [pdf] [Google scholar]

  • C. Gouriéroux, A. Monfort, and J.-P. Rennec. Identification and estimation in non-fundamental structural VARMA models. xx, 2017.
    [pdf] [Google scholar]

  • M. Lanne, M. Meitz and P. Saikkonen. Identification and estimation of non-Gaussian structural vector autoregressions. Journal of Econometrics, 196: 288-304, 2017.
    [pdf] [Google scholar]

  • M. Gong, K. Zhang, B. Schölkopf, C. Glymour, and D. Tao. Causal discovery from temporally aggregated time series. In Proc. 33rd Conference on Uncertainty in Artificial Intelligence (UAI2017), pp. xx-xx, Sydney, Australia, 2017.
    [pdf] [Google scholar]

  • T. H. Hai. Estimation of volatility causality in structural autoregressions with heteroskedasticity using independent component analysis. Statistical Papers, xx(xx): xx-xx, 2017.
    [pdf] [Google scholar]

  • S. Bauer, B. Schölkopf, and J. Peters. The arrow of time in multivariate time series. Arxiv preprint arXiv:1603.00784, 2016.
    [pdf] [Google scholar]

  • C. Gouriéroux, A. Monforta, and J.-P. Renne. Statistical inference for independent component analysis: Application to structural VAR models. Journal of Econometrics, xx(xx): xx-xx, 201x. Accepted.
    [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.
    [pdf] [Google scholar]

  • M. Kalli and J. E. Griffin. Bayesian nonparametric vector autoregressive models. xx, 2016.
    [pdf] [Google scholar]

  • M. Lanne and J. Luot. Data-driven inference on sign restrictions in Bayesian structural vector autoregression. CREATES Research Paper 2016-4, 2016.
    [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.
    [pdf] [Google scholar]

  • M. Gong, K. Zhang, B. Schölkopf, D. Tao, and P. Geiger. Discovering temporal causal relations from subsampled data. In Proc. 32nd International Conference on Machine Learning (ICML2015), pp. xx-xx, Lille, France, 2015.
    [pdf] [Google scholar]

  • L. Schiatti, G. Nollo, G. Rossato, and L. Faes. Extended Granger causality: A new tool to identify the structure of physiological networks. Physiological Measurement, 36: 827-843, 2015.
    [pdf] [Google scholar]

  • M. Lanne and P. Saikkonen. Noncausal vector autoregression. Econometric Theory, 29(3): 447-481, 2013.
    [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.
    [pdf] [Google scholar]

  • 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] [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.
    [pdf] [Google scholar]

  • L. Faes, S. Erla, A. Porta and G. Nollo. A framework for assessing frequency domain causality in physiological time series with instantaneous effects. Philosophical Transactions of the Royal Society A, 371: 20110618, 2013.
    [pdf] [Matlab code] [Google scholar]

  • L. Faes, S. Erla, E. Tranquillini, D. Orrico and G. Nollo. An identifiable model to assess frequency-domain Granger causality in the presence of significant instantaneous interactions. In Proc. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS2010), pp.1699-1702, Buenos Aires, Argentina, 2010.
    [pdf] [Google scholar]

  • A. Hyvärinen, K. Zhang, S. Shimizu, P. O. Hoyer. Estimation of a structural vector autoregressive model using non-Gaussianity. Journal of Machine Learning Research, 11(May): 1709−1731, 2010.
    [pdf] [Google scholar]
    R code by Doris Entner
    Matlab code by Luca Faes
    Python code by T. Ikeuchi and G. Haraoka

  • A. 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

  • 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]