Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Generalization of LiNGAM that allows confounding (2401.16661v3)

Published 30 Jan 2024 in cs.LG, cs.IT, math.IT, math.ST, and stat.TH

Abstract: LiNGAM determines the variable order from cause to effect using additive noise models, but it faces challenges with confounding. Previous methods maintained LiNGAM's fundamental structure while trying to identify and address variables affected by confounding. As a result, these methods required significant computational resources regardless of the presence of confounding, and they did not ensure the detection of all confounding types. In contrast, this paper enhances LiNGAM by introducing LiNGAM-MMI, a method that quantifies the magnitude of confounding using KL divergence and arranges the variables to minimize its impact. This method efficiently achieves a globally optimal variable order through the shortest path problem formulation. LiNGAM-MMI processes data as efficiently as traditional LiNGAM in scenarios without confounding while effectively addressing confounding situations. Our experimental results suggest that LiNGAM-MMI more accurately determines the correct variable order, both in the presence and absence of confounding.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (33)
  1. Markov equivalence for ancestral graphs. The Annals of Statistics, 37(5B):2808 – 2837, 2009. doi: 10.1214/08-AOS626. URL https://doi.org/10.1214/08-AOS626.
  2. Mutual information neural estimation. In International conference on machine learning, 2018.
  3. K. A. Bollen. Structural equations with latent variables. John Wiley & Sons, 1989.
  4. Causal structural learning via local graphs, 2021.
  5. Learning sparse causal models is not np-hard. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, UAI’13, page 172–181, Arlington, Virginia, USA, 2013. AUAI Press.
  6. Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, 40(1):294 – 321, 2012. doi: 10.1214/11-AOS940. URL https://doi.org/10.1214/11-AOS940.
  7. G. Darmois. Analyse générale des liaisons stochastiques: etude particulière de l’analyse factorielle linéaire. Revue de l’Institut International de Statistique / Review of the International Statistical Institute, 21(1/2):2–8, 1953. ISSN 03731138. URL http://www.jstor.org/stable/1401511.
  8. Doris Entner. Causal Structure Learning and Effect Identifcation in Linear Non-Gaussian Models and Beyond. PhD thesis, University of Helsinki, 01 2013.
  9. On causal discovery from time series data using fci. Probabilistic graphical models, pages 121–128, 2010.
  10. A kernel statistical test of independence. In J. Platt, D. Koller, Y. Singer, and S. Roweis, editors, Advances in Neural Information Processing Systems, volume 20. Curran Associates, Inc., 2007. URL https://proceedings.neurips.cc/paper/2007/file/d5cfead94f5350c12c322b5b664544c1-Paper.pdf.
  11. Estimation of causal effects using linear non-gaussian causal models with hidden variables. International Journal of Approximate Reasoning, 49(2):362–378, 2008. ISSN 0888-613X. doi: https://doi.org/10.1016/j.ijar.2008.02.006. URL https://www.sciencedirect.com/science/article/pii/S0888613X08000212. Special Section on Probabilistic Rough Sets and Special Section on PGM’06.
  12. Pairwise likelihood ratios for estimation of non-gaussian structural equation models. Journal of Machine Learning Research, 14(4):111–152, 2013. URL http://jmlr.org/papers/v14/hyvarinen13a.html.
  13. Estimating high-dimensional directed acyclic graphs with the pc-algorithm. Journal of Machine Learning Research, 8(3), 2007.
  14. Y. Kano and S. Shimizu. “Causal inference using non-normality”. In The International Symposium on Science of Modeling: The 30th Anniversary of the Information Criterion, pages 261–270, Washington DC, 12 2003.
  15. Estimating mutual information. Phys. Rev. E, 69:066138, Jun 2004. doi: 10.1103/PhysRevE.69.066138. URL https://link.aps.org/doi/10.1103/PhysRevE.69.066138.
  16. Jian Ma. copent: Estimating copula entropy and transfer entropy in r. arXiv:2005.14025, 2021.
  17. Mutual information is copula entropy. Tsinghua Science & Technology, 16(1):51–54, 2011. ISSN 1007-0214. doi: https://doi.org/10.1016/S1007-0214(11)70008-6. URL https://www.sciencedirect.com/science/article/pii/S1007021411700086.
  18. Rcd: Repetitive causal discovery of linear non-gaussian acyclic models with latent confounders. In Silvia Chiappa and Roberto Calandra, editors, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning Research, pages 735–745. PMLR, 26–28 Aug 2020. URL https://proceedings.mlr.press/v108/maeda20a.html.
  19. Judea Pearl. Causality: Models, Reasoning and Inference. Cambridge University Press, USA, 2nd edition, 2009. ISBN 052189560X.
  20. Richard Scheines Peter Spirtes, Clark Glymour. Causation, Prediction, and Search. Springer New York, NY, 1993.
  21. Learning linear non-gaussian causal models in the presence of latent variables. Journal of Machine Learning Research, 21(39):1–24, 2020. URL http://jmlr.org/papers/v21/19-260.html.
  22. Shohei 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 : JMLR, 15:2629–2652, 2014.
  23. A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(72):2003–2030, 2006. URL http://jmlr.org/papers/v7/shimizu06a.html.
  24. Directlingam: A direct method for learning a linear non-gaussian structural equation model. Journal of Machine Learning Research, 12(33):1225–1248, 2011. URL http://jmlr.org/papers/v12/shimizu11a.html.
  25. W. P. Skitovitch. On a property of the normal distribution. Doklady Akademii Nauk SSSR, 89:217–219, 1953.
  26. Martin J. Sklar. Fonctions de repartition a n dimensions et leurs marges. In Publications de l’Institut de Statistiquede l’Université de Paris, 1959.
  27. Causal inference in the presence of latent variables and selection bias. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, UAI’95, page 499–506, San Francisco, CA, USA, 1995. Morgan Kaufmann Publishers Inc. ISBN 1558603859.
  28. J Suzuki. Kernel Methods for Machine Learning with Math and R: 100 Exercises for Building Logic. Springer, 2022.
  29. Causal order identification to address confounding: binary variables. Behaviormetrika, 2022.
  30. ParceLiNGAM: A Causal Ordering Method Robust Against Latent Confounders. Neural Computation, 26(1):57–83, 01 2014. ISSN 0899-7667.
  31. Causal discovery with unobserved confounding and non-gaussian data. Journal of Machine Learning Research, 24(271):1–61, 2023. URL http://jmlr.org/papers/v24/21-1329.html.
  32. Jiji Zhang. On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence, 172(16-17):1873–1896, 2008. doi: 10.1016/j.artint.2008.08.001.
  33. gcastle: A python toolbox for causal discovery. ArXiv, abs/2111.15155, 2021.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now