Linear Latent confounders and latent factors

Linear Latent variables including latent confounders and latent factors

Models with latent confounding variables

• Y. Yang, M. Nafea, N. Kiyavash, K. Zhang, A. E. Ghassami. Discovery and inference of possibly bi-directional causal relationships with invalid instrumental variables. arXiv:2407.19426, 2024.
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• W. Li, R. Duan, S. Li. Discovery and inference of possibly bi-directional causal relationships with invalid instrumental variables. arXiv:2405.15325, 2024.
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• R. Massidda, S. Magliacane, D. Bacciu. On the Identification of Temporally Causal Representation with Instantaneous Dependence. arXiv:2406.00394, 2024.
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• Z. Li, Y. Shen, K. Zheng, R. Cai, X. Song, M. Gong, Z. Zhu, G. Chen, K. Zhang. On the Identification of Temporally Causal Representation with Instantaneous Dependence. arXiv:2405.15325, 2024.
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• Y. Liu, Z. Zhang, D. Gong, M. Gong, B. Huang, A. van den Hengel, K. Zhang, J. Q. Shi. Identifiable Latent Neural Causal Models. arXiv preprint arXiv:2403.15711, 2024.
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• J. Suzuki, T.-L. Yang. Generalization of LiNGAM that allows confounding. arXiv preprint arXiv:2401.16661, 2024.
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• K. Wang, A. Seigal. Identifiability of overcomplete independent component analysis. arXiv preprint arXiv:2401.14709.
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• X. Dong, B. Huang, I. Ng, X. Song, Y. Zheng, S. Jin, R. Legaspi, P. Spirtes, K. Zhang. Some General Identification Results for Linear Latent Hierarchical Causal Structure. arXiv preprint arXiv:2312.11001, 2023.
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• Z. Chen, F. Xie, J. Qiao, Z. Hao, R. Cai. Some General Identification Results for Linear Latent Hierarchical Causal Structure. Proc. Thirty-Second International Joint Conference on Artificial Intelligence, Pages 3568-3576, 2023.
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• F. Xie, B. Huang, Z. Chen, R. Cai, C. Glymour, Z. Geng, K. Zhang. Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables. arXiv preprint arXiv:2308.06718, 2023.
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• R. Cai, Z. Huang, W. Chen, Z. Hao, K. Zhang. Sample-Specific Root Causal Inference with Latent Variables. arXiv:2305.19582, 2023. 
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• Genin, K. and Mayo-Wilson, C. Success concepts for causal discovery. Behaviormetrika, xx:xx-xx, 2022.  
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• E. V. Strobl, T. A. Lasko. Sample-Specific Root Causal Inference with Latent Variables. arXiv:2210.01798, 2022. 
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• B. Huang, C. Jia Han Low, F. Xie, C. Glymour, K. Zhang. Latent Hierarchical Causal Structure Discovery with Rank Constraints. arXiv:2210.01798, 2022. 
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• Y. Liu, Z. Zhang, D. Gong, M. Gong, B. Huang, A. van den Hengel, K. Zhang, J. Q. Shi. Weight-variant Latent Causal Models. arXiv:2201.12392, 2022. 
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• Z. Tamimy, E. van Bergen, M. D. van der Zee, C. V. Dolan, M. G. Nivard. Multi Co-Moment Structural Equation Models: Discovering Direction of Causality in the Presence of Confounding. SocArXiv, 2022. 
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• F. Zhou, K. He, Y. Ni. Causal Discovery with Heterogeneous Observational Data. arXiv:2201.12392, 2022. 
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• J. Adams, N. Hansen, K. Zhang . Identification of Partially Observed Linear Causal Models: Graphical Conditions for the Non-Gaussian and Heterogeneous Cases.  In Advances in Neural Information Processing Systems 35 (NeurIPS2021), pp. xx-xx, 2021.
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• W. Chen, R. Cai, K. Zhang, Z. Hao. Causal Discovery in Linear Non-Gaussian Acyclic Model With Multiple Latent Confounders. IEEE Transactions on Neural Networks and Learning Systems, xx(x): xx-xx, 2021.[pdf] [Google scholar]

• Y. Liu, E. Robeva, and H. Wang. Learning Linear Non-Gaussian Graphical Models with Multidirected Edges. arXiv:2010.05306 , 2020. 
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• S. Salehkaleybar, A. Ghassami, N. Kiyavash, K. Zhang. Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables. Journal of Machine Learning Research, 21:1-24, 2020.  
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• Y. S. Wang, M. Drton. Causal Discovery with Unobserved Confounding and non-Gaussian Data. arXiv:2007.11131, 2020. 
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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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• 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.
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  Python code by Taku Yoshioka
  Python code by Akimitsu Inoue

• 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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• Z. Chen and L. Chan. Causality in linear nongaussian acyclic models in the presence of latent Gaussian confounders. Neural Computation, 25(6): 1605-1641, 2013.
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• Z. Chen and L. Chan. Causal discovery for linear non-Gaussian acyclic models in the presence of latent Gaussian confounders. In Proc. 10th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA2012), Tel Aviv, Israel, pp.17--24, 2012.
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• 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.
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• P. O. Hoyer, S. Shimizu and A. Kerminen. Estimation of linear, non-gaussian causal models in the presence of confounding latent variables. In Proc. the third European Workshop on Probabilistic Graphical Models (PGM2006), pp. 155--162, Prague, Czech Republic, 2006.
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Estimation of models with latent confounding

• Y. Morinishi and S. Shimizu. Differentiable causal discovery of linear non-Gaussian acyclic models under unmeasured confounding. Arxiv preprint arXiv: 2501.12854, 2025.
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• D. Schkoda, E. Robeva, M. Drton. Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding. arXiv:2408.04907, 2024.
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• H. J. J. Ong, B. G. S. Lim. Redefining the Shortest Path Problem Formulation of the Linear Non-Gaussian Acyclic Model: Pairwise Likelihood Ratios, Prior Knowledge, and Path Enumeration. arXiv:2404.11922, 2024.
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• W. Chen, Z. Huang, R. Cai, Z. Hao, K. Zhang. Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants. arXiv:2312.11934, 2023.
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• B. Zhang, W. Wiedermann. Covariate selection in causal learning under non-Gaussianity. Behavior Research Methods, xx(xx): xx--xx, 2023.
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• C. Schultheiss, P. Bühlmann, M. Yuan. Higher-order least squares: assessing partial goodness of fit of linear causal models. Journal of the American Statistical Association, xx(xx): 1--27, 2022.
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• T. N. Maeda. I-RCD: an improved algorithm of repetitive causal discovery from data with latent confounders. Behaviormetrika, xx(xx): xx--xx, 2022.
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• W. Chen, K. Zhang, R. Cai, B. Huang, J. Ramsey, Z. Hao, C. Glymour. FRITL: A Hybrid Method for Causal Discovery in the Presence of Latent Confounders. Arxiv preprint  arXiv:2103.14238, 2021. 
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• E. Robeva, J.-B. Seby. Multi-trek separation in Linear Structural Equation Models. Arxiv preprint  arXiv:2001.10426, 2020. 
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• T. N. Maeda, S. Shimizu. RCD: Repetitive causal discovery of linear non-Gaussian acyclic models with latent confounders. In Proc. 23rd International Conference on Artificial Intelligence and Statistics (AISTATS2020), Palermo, Sicily, Italy. PMLR: Volume xx.
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  Python code

• C. Ding, M. Gong, K. Zhang, D. Tao. Likelihood-Free Overcomplete ICA and Applications in Causal Discovery. In Advances in Neural Information Processing Systems 33 (NIPS2019), pp. xx-xx, 2019.
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• S. Shimizu. A non-Gaussian approach for causal discovery in the presence of hidden common causes. In Proc. Second Workshop on Advanced Methodologies for Bayesian Networks (AMBN2015), pp. 222--233, Yokohama, Japan, 2015.
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• 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.
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• T. Tashiro, S. Shimizu, A. Hyvärinen and T. Washio. Estimation of causal orders in a linear non-Gaussian acyclic model: a method robust against latent confounders. In Proc. 22nd International Conference on Artificial Neural Networks (ICANN2012), pp. 491--498, Lausanne, Switzerland, 2012.
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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. Entner and P. O. Hoyer. Discovering unconfounded causal relationships using linear non-Gaussian models.  New Frontiers in Artificial Intelligence, Lecture Notes in Computer Science, 6797: 181-195, 2011.
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Others

• L. Kong, B. Huang, F. Xie, E. Xing, Y. Chi, K. Zhang. Identification of Nonlinear Latent Hierarchical Models. arXiv preprint arXiv:2306.07916, 2023.  
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• F. Xie, Y. Zeng, Z. Chen, Y. He, Z. Geng, K. Zhang. Causal discovery of 1-factor measurement models in linear latent variable models with arbitrary noise distributions. Neurocomputing, xx:xx-xx, 2023.  
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• H. Dai, P. Spirtes, K. Zhang. Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models. ArXiv preprint arXiv:2210.11021, 2022.
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• F. Xie, B. Huang, Z. Chen, Y. He, Z. Geng, K. Zhang. Identification of Linear Non-Gaussian Latent Hierarchical Structure. In Proc. 39th International Conference on Machine Learning, PMLR 162:24370-24387, 2022.
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• Z. Chen, F. Xie, J. Qiao, Z. Hao, K. Zhang, R. Cai. Identification of Linear Latent Variable Model with Arbitrary Distribution. In Proc. 36th AAAI Conference on Artificial Intelligence (AAAI2022), pp. xx-xx, 2022.
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• X. Li, M. P. Martens, W. Wiedermann. Conditional Direction of Dependence Modeling: Application and Implementation in SPSS. Social Science Computer Review, xx(xx): xx-xx, 2022.
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• V. P. Nia, X. Li, M. Asgharian, S. Hu, Y.  Geng, Z.  Chen. A causal direction test for heterogeneous populations. Machine Learning with Applications, xx(xx): xx-xx, 2021.
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• W. Chen, Y. Wu, R. Cai, Y. Chen, Z. Hao. CCSL: A Causal Structure Learning Method from Multiple Unknown Environments. ArXiv preprint arXiv:2111.09666, 2021.
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• W. Yao, Y. Sun, A. Ho, C. Sun, K. Zhang. Learning Temporally Causal Latent Processes from General Temporal Data. ArXiv preprint arXiv:2110.05428, 2021.
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• F. Xie, R. Cai, B. Huang, C. Glymour, Z. Hao, K. Zhang. Generalized Independent Noise Condition for Estimating Linear Non-Gaussian Latent Variable Graphs.  In Advances in Neural Information Processing Systems 34 (NeurIPS2020), pp. xx-xx, 2020.
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• Y. Zeng, S. Shimizu, R. Cai, F. Xie, M. Yamamoto, Z. Hao. Causal Discovery with Multi-Domain LiNGAM for Latent Factors. In Proc. 30th International Joint Conference on Artificial Intelligence (IJCAI-21), 2021.
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  Python code

• M.P. van Wie, X. Li, W. Wiedermann. Identification of confounded subgroups using linear model-based recursive partitioning. Psychological Test and Assessment Modeling, 61(4): 365-387, 2019.[
  pdf] [Google scholar]

• R. Cai, F. Xie, C. Glymour, Z. Hao, K. Zhang. Triad Constraints for Learning Causal Structure of Latent Variables. In Advances in Neural Information Processing Systems 33 (NeurIPS2019), pp. xx-xx, 2019.
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• F. Xie, R. Cai, Y. Zeng, J. Gao, Z. Hao. An Efficient Entropy-Based Causal Discovery Method for Linear Structural Equation Models With IID Noise Variables. IEEE Transactions on Neural Networks and Learning Systems, xx: xx-xx, 2019.
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• K. Zhang, M. Gong, J. Ramsey, K. Batmanghelich, P. Spirtes, and C. Glymour. Causal discovery in the presence of measurement error: Identifiability conditions. In Proc. 34th Conf. on Uncertainty in Artificial Intelligence (UAI2018), pp. xx-xx, Montreal, Canada, 2018.
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• R. Pio Monti, A. Hyvärinen. A unified probabilistic model for learning latent factors and their connectivities from high-dimensional data.  In Proc. 34th Conf. on Uncertainty in Artificial Intelligence (UAI2018), pp. xx-xx, Montreal, Canada, 2018.
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• N. Tanaka, S. Shimizu, and T. Washio. A Bayesian estimation approach to analyze non-Gaussian data-generating processes with latent classes. Arxiv preprint arXiv:1408.0337, 2014.
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• A. von Eye and W. Wiedermann. On direction of dependence in latent variable contexts. Educational and Psychological Measurement, 74(1): 5-30, 2014.
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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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• 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.
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• S. Shimizu, P. O. Hoyer and A. Hyvärinen. Estimation of linear non-Gaussian acyclic models for latent factors.Neurocomputing, 72: 2024-2027, 2009.
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• S. Shimizu and A. Hyvärinen. Discovery of linear non-gaussian acyclic models in the presence of latent classes. In Proc. 14th Int. Conf. on Neural Information Processing (ICONIP2007), pp. 752-761, Kitakyushu, Japan, 2008.
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