Basic linear models

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

Acyclic models

Model

• 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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• J. Qiao, Y. Xiang, Z. Chen, R. Cai, and Z. Hao. Causal Discovery from Poisson Branching Structural Causal Model Using High-Order Cumulant with Path Analysis. In Proc. AAAI Conference on Artificial Intelligence, 38(18), 20524-20531, 2024.
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• T.-L. Yang, K. Y. Lee, K. Zhang, J. Suzuki. Functional Linear Non-Gaussian Acyclic Model for Causal Discovery. arXiv:2401.09641, 2024.
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• Y. Cai, X Li, M Sun, P Li. Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrix. arXiv:2311.00674, 2023.
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• J. Wu, M. Drton. Partial Homoscedasticity in Causal Discovery with Linear Models. ArXiv preprint arXiv:2308.08959, 2023.
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• P Misiakos, C Wendler, M Püschel. Learning DAGs from Data with Few Root Causes. Arxiv preprint arXiv preprint arXiv:2305.15936, 2023.
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• A. Dallakyan. On Learning Time Series Summary DAGs: A Frequency Domain Approach. Arxiv preprint arXiv:2304.08482, 2023.
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• F. Zhou, K. He, Y. Ni. Individualized causal discovery with latent trajectory embedded bayesian networks. Biometrics, xx: xx--xx, 2023.
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• 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.
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• G. Park. Identifiability of Additive Noise Models Using Conditional Variances. Journal of Machine Learning Research, 21: 1--34, 2020.
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• 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.
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• S. Yu, M. Drton, A. Shojaie. Directed Graphical Models and Causal Discovery for Zero-Inflated Data. Arxiv preprint  arXiv:2004.04150, 2020. 
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• N. Gnecco, N. Meinshausen, J. Peters, S. Engelke. Causal discovery in heavy-tailed models. Arxiv preprint  arXiv:1908.05097, 2019.  
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• W. Wiedermann and A. von Eye. Testing the causal direction of mediation effects in randomized intervention studies. Prevention Science, xx(xx): xx--xx, 2018.
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• A Ghoshal and J Honorio. Learning identifiable Gaussian Bayesian networks in polynomial time and sample complexity. Arxiv preprint arXiv:1703.01196, 2017.
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• A. Ghoshal and J. Honorio. Learning linear structural equation models in polynomial time and sample complexity. Arxiv preprint arXiv:1707.04673, 2017.
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• W. Wiedermann and A. von Eye. Direction of effects in mediation analysis. Psychological Methods, 20(2): 221--244, 2015.
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• W. Wiedermann and A. von Eye. Direction of effects in multiple linear regression models. Multivariate Behavioral Research, 50(1): 23--40, 2015.
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• A. Sokol, M. H. Maathuis and B. Falkeborg. Quantifying identifiability in independent component analysis. Electronic Journal of Statistics, 8: 1438--1459, 2014.
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• J. Peters and P. Bühlmann. Identifiability of Gaussian structural equation models with equal error variances. Biometrika, 101(1): 219--228, 2014.
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• 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.
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• 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.
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  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.
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• Y. Dodge and V. Rousson. On asymmetric properties of the correlation coefficient in the regression setting.
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• Y. Dodge and V. Rousson. Direction dependence in a regression line. Communications in Statistics - Theory and Methods, 29(9-10): 1957--1972, 2000.
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Estimation

• NEW J. Raymaekers. Robustness in LiNGAM. In: Combining, Modelling and Analyzing Imprecision, Randomness and Dependence. SMPS 2024. Advances in Intelligent Systems and Computing, vol 1458, 2024.
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• NEW A. Trilla, N. Mijatovic. Unsupervised Pairwise Causal Discovery on Heterogeneous Data using Mutual Information Measures. In Proc. 26th International Conference of the Catalan Association for Artificial Intelligence, 2024.
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• S. Hiremath, J. R. M. A. Maasch, M. Gao, P. Ghosal, K. Gan. Hybrid Global Causal Discovery with Local Search. arXiv:2405.14496, 2024.
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• A. Shojaie, W. Chen. Learning Directed Acyclic Graphs From Partial Orderings. arXiv preprint arXiv:2403.14125, 2024.
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• M. Cai and H. Hara. Learning causal graphs using variable grouping according to ancestral relationship. arXiv preprint arXiv:2403.14125, 2024.
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• V. Akinwande, J. Z. Kolter. AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUs. arXiv:2403.03772, 2024.
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• M. de Mier, F. Delbianco, F. Tohmé, L. Patrizio, F. Rodriguez,  M. R. Stéfani. Causality by Vote: Aggregating Evidence on Causal Relations in Economic Growth Processes. Documento de trabajo RedNIE N°260, 2023.
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• S. Hwang, K. Lee, S. Oh, G. Park. Bayesian Approach to Linear Bayesian Networks. arXiv:2311.15610, 2023.
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• J. Lin, H. Lei, G. Michailidis. Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees. arXiv:2311.15434, 2023.
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• A. Vashishtha, A. G. Reddy, A. Kumar, S. Bachu, V. N. Balasubramanian, A. Sharma. Causal Inference Using LLM-Guided Discovery. arXiv:2310.15117, 2023.
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• S. Leyder, J. Raymaekers, T. Verdonck. TSLiNGAM: DirectLiNGAM under heavy tails. arXiv:2308.05422, 2023.
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• Y. Hong, J. Guo, G. Mai, Y. Lin, H. Zhang, Z. Hao, G. Zheng. High-dimensional causal discovery based on heuristic causal partitioning. Applied Intelligence, xx:xx-xx, 2023.
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• 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.
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• I. Ng, B. Huang, K. Zhang. Structure Learning with Continuous Optimization: A Sober Look and Beyond. arXiv:2304.02146, 2023.
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• C. Deidda, S. Engelke, C. De Michele. Asymmetric dependence in hydrological extremes. Journal of Statistical Computation and Simulation, 2023.
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• K. Matsuda, K. Kurihara, K. Kawakami, M. Yamazaki, F. Yamada, T. Tabaru, and K. Yokoyama. Accelerating LiNGAM Causal Discovery with Massive Parallel Execution on Supercomputer Fugaku. IEICE TRANSACTIONS on Information and Systems, E105-D(12): 2032-2039, 2022.
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• T. Yang and J. Suzuki. The Functional LiNGAM. In Proc. 11th International Conference on Probabilistic Graphical Models (PGM2022), PMLR 186:25-36, 2022.
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• D. Tramontano, A. Monod, M. Drton. Learning Linear Non-Gaussian Polytree Models. In Proc. 38th Conference on Uncertainty in Artificial Intelligence (UAI2022), pp. xx-xx, 2022.
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• C. Schultheiss, P. Bühlmann. Ancestor regression in linear structural equation models. arXiv:2205.08925, 2022.
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• 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.
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• S. Dong, M. Sebag. From graphs to DAGs: a low-complexity model and a scalable algorithm. arXiv:2204.04644, 2022.
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• 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.
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• 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.
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• 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.
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• 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.
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• A. Shahbazinia, S. Salehkaleybar, M. Hashemi. ParaLiNGAM: Parallel Causal Structure Learning for Linear non-Gaussian Acyclic Models. Arxiv preprint arXiv:2109.13993, 2021. 
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• K. Harada, H. Fujisawa. Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery. Neurocomputing, xx(x): xx-xx, 2021.
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• 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.
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• M. Kaiser, M. Sipos. Unsuitability of NOTEARS for Causal Graph Discovery. Arxiv preprint arXiv:2104.05441, 2021. 
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• 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. 
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• 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. 
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• 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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• 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.
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• 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.
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• 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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• 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.
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• 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.
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• 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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• 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.
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• 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.
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• 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.
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• 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.
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• 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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• 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.
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• 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.
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• 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.
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• 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.
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• F. Thoemmes. Empirical evaluation of directional-dependence tests. International Journal of Behavioral Development, xx(xx): xx--xx, 2015. In press.
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• 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.
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• 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.
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• 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.
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• 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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• Y. Dodge and I. Yadegari. On direction of dependence. Metrika, 72: 139--150, 2010.
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• R. Henao and O. Winther. Sparse linear identifiable multivariate modeling. Journal of Machine Learning Research, 12(Mar): 863--905, 2011.
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• 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.
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• 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.
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• 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.
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• 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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• 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.
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• 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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• 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.
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• 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)
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• 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.
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• A. B. Nielsen and L. K. Hansen. Structure learning by pruning in independent component analysis. Neurocomputing, 71: 2281--2290, 2008.
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• 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.
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• 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

• T. Nakanishi. The NG-SVAR Model under the Pearson Family of Distributions: Implementation with R Packages. Journal of International Economic Studies, 38: 35‒46, 2024.
  [pdf] [Google scholar]

• 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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• C. K. Assaad, D. Bystrova, J. Arbel, E. Devijver, E. Gaussier, W. Thuiller. Hybrids of Constraint-based and Noise-based Algorithms for Causal Discovery from Time Series. Arxiv preprint arXiv:22306.08765, 2022.
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• K. Maekawa, T. Nakanishi. Estimation of non-Gaussian SVAR models: a pseudo-log-likelihood function approach. Journal of Statistical Computation and Simulation, xx: xx-xx, 2022.
  [pdf] [Google schlar]

• A. Einizade, S. H. Sardouie. Estimation of a Causal Directed Acyclic Graph Process using Non-Gaussianity. Arxiv preprint arXiv:2211.13800, 2022.
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• L. Hoesch, A. Lee, G. Mesters. Robust Inference for Non-Gaussian SVAR models. Economics Working Paper Series Working Paper No. 1847, 2022.
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• S. Lee, S. Lee, K. Maekawa. Change point test for structural vector autoregressive model via independent component analysis. Journal of Statistical Computation and Simulation, xx(xx): xx-xx, 2022.
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• G. Bormetti, F. Corsi. A Lucas Critique Compliant SVAR model with Observation-driven Time-varying Parameters. Arxiv preprint arXiv:2107.05263, 2021.
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• M. Lanne, J. Luoto. GMM Estimation of Non-Gaussian Structural Vector Autoregression. Journal of Business & Economic Statistics, 39(1): 69-81, 2021.
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• S. M.  Zema. Non-Normal Identification for Price Discovery in High-Frequency Financial Markets. LEM Working Paper Series, ISSN(ONLINE) 2284-0400, 2020. 
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• C. Velasco. Identification and estimation of Structural VARMA models using higher order dynamics. Arxiv preprint arXiv:2009.04428, 2020. 
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• 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.
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• 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.  
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• 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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• 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.
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• 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.
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• 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.
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• C. Gouriéroux, A. Monfort, and  J.-P. Rennec. Identification and estimation in non-fundamental structural VARMA models. xx, 2017.
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• M. Lanne, M. Meitz and P. Saikkonen. Identification and estimation of non-Gaussian structural vector autoregressions. Journal of Econometrics, 196: 288-304, 2017.
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• 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.
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• T. H. Hai. Estimation of volatility causality in structural autoregressions with heteroskedasticity using independent component analysis. Statistical Papers, xx(xx): xx-xx, 2017. 
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• 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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• 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.
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• 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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• M. Kalli and J. E. Griffin. Bayesian nonparametric vector autoregressive models. xx, 2016.
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• M. Lanne and J. Luot. Data-driven inference on sign restrictions in Bayesian structural vector autoregression. CREATES Research Paper 2016-4, 2016.
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• M. Lanne, M. Meitz, and P. Saikkon. Identification and estimation of non-Gaussian structural vector autoregressions. CREATES Research Paper 2015-1, 2015.
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• 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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• 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.
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• 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.
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• 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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• 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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• 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.
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• 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.
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• 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.
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• 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.
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Others

• K. Du, Y. Xiang . Causal Inference Using Linear Time-Varying Filters with Additive Noise. Arxiv preprint arXiv:2012.13025, 2020. 
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• 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.
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• 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.
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• 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.
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• 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.
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• R. Henao and O. Winther. Sparse linear identifiable multivariate modeling. Journal of Machine Learning Research, 12(Mar): 863--905, 2011.
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• D. Janzing. On the entropy production of time series with unidirectional linearity. Journal of Statistical Physics, 138(4-5): 767-779, 2010.
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• 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.
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Cyclic models

• H. Dai, I. Ng, Y. Zheng, Z. Gao, K. Zhang.  Local Causal Discovery with Linear non-Gaussian Cyclic Models. arXiv:2403.14843, 2024.
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• S. Roy, R. K. W. Wong, Y. Ni. Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data. arXiv:2310.20537, 2023.
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• M. Drton, B. Hollering, J. Wu. Identifiability of Homoscedastic Linear Structural Equation Models using Algebraic Matroids. arXiv:2308.01821, 2013.
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• 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.
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• 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.
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• 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.
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