Causal discovery with continuous additive noise models

Journal of Machine Learning Research

Volumn 15, Issue , 2014, Pages 2009-2053

  Peters, Jonas ^a   Mooij, Joris M ^b,c   Janzing, Dominik ^d   Schölkopf, Bernhard ^d  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

^c RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^d MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Additive noise; Bayesian networks; Causal inference; Causal minimality; Identifiability; Structural equation models

Indexed keywords

BAYESIAN NETWORKS; BEHAVIORAL RESEARCH; EQUIVALENCE CLASSES; GRAPH THEORY; TELECOMMUNICATION SERVICES;

CAUSAL INFERENCES; DIRECTED ACYCLIC GRAPH (DAG); EMPIRICAL EVALUATIONS; IDENTIFIABILITY; MARKOV EQUIVALENCE CLASS; MINIMALITY; STRUCTURAL EQUATION MODELING; STRUCTURAL EQUATION MODELS;

ADDITIVE NOISE;

EID: 84904201625     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (67)

1. S. Acid and L. M. de Campos. Searching for Bayesian network structures in the space of restricted acyclic partially directed graphs. Journal of Artificial Intelligence Research, 18:445-490, 2003. (Pubitemid 41525942)
2. W. P. Bergsma. Testing Conditional Independence for Continuous Random Variables, 2004. EURANDOM-report 2004-049.
3. K. A. Bollen. Structural Equations with Latent Variables. John Wiley & Sons, 1989.
4. P. Bühlmann, J. Peters, and J. Ernest. CAM: Causal additive models, high-dimensional order search and penalized regression. ArXiv e-prints (1207.5136), 2013.
5. D. M. Chickering. A transformational characterization of equivalent Bayesian network structures. In Proceedings of the 11th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 1995.
6. D. M. Chickering. Learning Bayesian networks is NP-complete. In Learning from Data: Artificial Intelligence and Statistics V. Springer-Verlag, 1996.
7. D. M. Chickering. Optimal structure identification with greedy search. Journal of Machine Learning Research, 3:507-554, 2002.
8. P. Comon. Independent component analysis - a new concept? Signal Processing, 36: 287-314, 1994.
9. G. Darmois. Analyse générale des liaisons stochastiques. Revue de l'Institut International de Statistique, 21:2-8, 1953.
10. A. P. Dawid. Conditional independence in statistical theory. Journal of the Royal Statistical Society. Series B, 41(1):1-31, 1979.
11. Deutscher Wetterdienst. Climate data. http://www.dwd.de/, 2008.
12. M. J. Druzdzel and H. van Leijen. Causal reversibility in Bayesian networks. Journal of Experimental and Theoretical Artificial Intelligence, 13(1):45-62, 2001.
13. F. Eberhardt and R. Scheines. Interventions and causal inference. Philosophy of Science, 74(5):981-995, 2007.
14. N. Friedman and D. Koller. Being Bayesian about Bayesian network structure: A Bayesian approach to structure discovery in Bayesian networks. Machine Learning, 50:95-125, 2003.
15. K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf. Kernel measures of conditional dependence. In Advances in Neural Information Processing Systems 20 (NIPS), 2008.
16. D. Geiger and D. Heckerman. Learning Gaussian networks. In Proceedings of the 10th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 1994.
17. A. Gretton, R. Herbrich, A. Smola, O. Bousquet, and B. Schölkopf. Kernel methods for measuring independence. Journal of Machine Learning Research, 6:2075-2129, 2005. (Pubitemid 41798124)
18. A. Gretton, K. Fukumizu, C. H. Teo, L. Song, B. Schölkopf, and A. Smola. A kernel statistical test of independence. In Advances in Neural Information Processing Systems 20 (NIPS), 2008.
19. D. M. A. Haughton. On the choice of a model to fit data from an exponential family. The Annals of Statistics, 16:342-355, 1988.
20. D. Heckerman. A Bayesian approach to causal discovery. Technical report, Microsoft Research (MSR-TR-97-05), 1997.
21. D. Heckerman and D. Geiger. Likelihoods and parameter priors for Bayesian networks. Technical report, Microsoft Research (MSR-TR-95-54), 1995.
22. P. Hoyer, S. Shimizu, A. J. Kerminen, and M. Palviainen. Estimation of causal effects using linear non-Gaussian causal models with hidden variables. International Journal of Approximate Reasoning, 49:362-378, 2008.
23. P. Hoyer, D. Janzing, J. M. Mooij, J. Peters, and B. Schölkopf. Nonlinear causal discovery with additive noise models. In Advances in Neural Information Processing Systems 21 (NIPS), 2009.
24. A. Hyvärinen and S. M. Smith. Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. Journal of Machine Learning Research, 14:111-152, 2013.
25. D. Janzing and B. Schölkopf. Causal inference using the algorithmic Markov condition. IEEE Transactions on Information Theory, 56:5168-5194, 2010.
26. D. Janzing and B. Steudel. Justifying additive-noise-model based causal discovery via algorithmic information theory. Open Systems and Information Dynamics, 17:189-212, 2010.
27. D. Janzing, J. Peters, J. M. Mooij, and B. Schölkopf. Identifying confounders using additive noise models. In Proceedings of the 25th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2009.
28. M. Kalisch and P. Bühlmann. Estimating high-dimensional directed acyclic graphs with the PC-algorithm. Journal of Machine Learning Research, 8:613-636, 2007. (Pubitemid 46473523)
29. Y. Kano and S. Shimizu. Causal inference using nonnormality. In Proceedings of the International Symposium on Science of Modeling, the 30th Anniversary of the Information Criterion, Tokyo, Japan, 2003.
30. D. Koller and N. Friedman. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009.
31. S. Lauritzen. Graphical Models. Oxford University Press, New York, 1996.
32. C. Meek. Graphical Models: Selecting Causal and Statistical Models. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, 1997.
33. J. M. Mooij and D. Janzing. Distinguishing between cause and effect. Journal of Machine Learning Research W&CP, 6:147-156, 2010.
34. J. M. Mooij, D. Janzing, J. Peters, and B. Schölkopf. Regression by dependence minimization and its application to causal inference. In Proceedings of the 26th International Conference on Machine Learning (ICML), 2009.
35. J. M. Mooij, D. Janzing, T. Heskes, and B. Schölkopf. On causal discovery with cyclic additive noise models. In Advances in Neural Information Processing Systems 24 (NIPS), 2011.
36. J. M. Mooij, D. Janzing, and B. Schölkopf. From ordinary differential equations to structural causal models: the deterministic case. In Proceedings of the 29th Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2013.
37. C. Nowzohour and P. Bühlmann. Score-based causal learning in additive noise models. ArXiv e-prints (1311.6359), 2013.
38. OEIS Foundation Inc. The on-line encyclopedia of integer sequences. http://oeis.org/ A003024, 2011.
39. J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2nd edition, 2009.
40. J. Peters. Asymmetries of time series under inverting their direction. Diploma Thesis, University of Heidelberg, 2008. http://stat.ethz.ch/people/ jopeters.
41. J. Peters. Restricted Structural Equation Models for Causal Inference. PhD thesis, ETH Zurich and MPI for Intelligent Systems, 2012. http://dx.doi.org/10.3929/ethz-a-007597940.
42. J. Peters. On the intersection property of conditional independence and its application to causal discovery. ArXiv e-prints (1403.0408), 2014.
43. J. Peters and P. Bühlmann. Structural intervention distance (SID) for evaluating causal graphs. ArXiv e-prints (1306.1043), 2013.
44. J. Peters and P. Bühlmann. Identifiability of Gaussian structural equation models with equal error variances. Biometrika, 101:219-228, 2014.
45. J. Peters, D. Janzing, and B. Schölkopf. Causal inference on discrete data using additive noise models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33: 2436-2450, 2011a.
46. J. Peters, J. M. Mooij, D. Janzing, and B. Schölkopf. Identifiability of causal graphs using functional models. In Proceedings of the 27th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2011b.
47. J. Ramsey, J. Zhang, and P. Spirtes. Adjacency-faithfulness and conservative causal inference. In Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2006.
48. C. E. Rasmussen and H. Nickisch. Gaussian processes for machine learning (GPML) toolbox. Journal of Machine Learning Research, 11:3011-3015, 2010.
49. T. Richardson and P. Spirtes. Ancestral graph Markov models. Annals of Statistics, 30(4): 962-1030, 2002. (Pubitemid 37095336)
50. B. Schölkopf, D. Janzing, J. Peters, E. Sgouritsa, K. Zhang, and J. M. Mooij. On causal and anticausal learning. In Proceedings of the 29th International Conference on Machine Learning (ICML), 2012.
51. S. Shimizu, P. Hoyer, A. Hyvärinen, and A. J. Kerminen. A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7:2003-2030, 2006. (Pubitemid 44497456)
52. S. Shimizu, T. Inazumi, Y. Sogawa, A. Hyvärinen, Y. Kawahara, T. Washio, P. Hoyer, and K. Bollen. DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. Journal of Machine Learning Research, 12:1225-1248, 2011.
53. R. Silva and Z. Ghahramani. The hidden life of latent variables: Bayesian learning with mixed graph models. Journal of Machine Learning Research, 10:1187-1238, 2009.
54. V.P. Skitovič. Linear forms in independent random variables and the normal distribution law (in Russian). Izvestiia AN SSSR, Ser. Matem., 18:185-200, 1954.
55. V.P. Skitovič. Linear combinations of independent random variables and the normal distribution law. Select. Transl. Math. Stat. Probab., 2:211-228, 1962.
56. P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search. MIT Press, 2nd edition, 2000.
57. Y. Tamada, S. Imoto, H. Araki, M. Nagasaki, C. G. Print, S. D. Charnock-Jones, and S. Miyano. Estimating genome-wide gene networks using nonparametric Bayesian network models on massively parallel computers. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8(3):683-697, 2011a.
58. Y. Tamada, S. Imoto, and S. Miyano. Parallel algorithm for learning optimal Bayesian network structure. Journal of Machine Learning Research, 12:2437-2459, 2011b.
59. M. Teyssier and D. Koller. Ordering-based search: a simple and effective algorithm for learning Bayesian networks. In Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI), 2005.
60. I. Tsamardinos, L. E. Brown, and C. F. Aliferis. The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 65(1):31-78, 2006. (Pubitemid 44451193)
61. C. Uhler, G. Raskutti, P. Bühlmann, and B. Yu. Geometry of the faithfulness assumption in causal inference. Annals of Statistics, 41(2):436-463, 2013.
62. T. Verma and J. Pearl. Equivalence and synthesis of causal models. In Proceedings of the 6th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 1991.
63. S. Wright. Correlation and causation. Journal of Agricultural Research, 20:557-585, 1921.
64. J. Zhang and P. Spirtes. Strong faithfulness and uniform consistency in causal inference. In Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2003.
65. J. Zhang and P. Spirtes. Detection of unfaithfulness and robust causal inference. Minds and Machines, 18:239-271, 2008.
66. K. Zhang and A. Hyvärinen. On the identifiability of the post-nonlinear causal model. In Proceedings of the 25th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2009.
67. K. Zhang, J. Peters, D. Janzing, and B. Schölkopf. Kernel-based conditional independence test and application in causal discovery. In Proceedings of the 27th Annual Conference on Uncertainty in Artificial Intelligence (UAI), 2011.