High-dimensional learning of linear causal networks via inverse covariance estimation

Journal of Machine Learning Research

Volumn 15, Issue , 2015, Pages 3065-3105

  Loh, Po Ling ^a   Büuhlmann, Peter ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Causal inference; Dynamic programming; Identifiability; Inverse covariance matrix estimation; Linear structural equation models

Indexed keywords

BEHAVIORAL RESEARCH; COVARIANCE MATRIX; DIRECTED GRAPHS; MATHEMATICAL MODELS; TELECOMMUNICATION SERVICES;

CAUSAL INFERENCES; DIRECTED ACYCLIC GRAPHS; HIGH-DIMENSIONAL LEARNING; IDENTIFIABILITY; INVERSE COVARIANCE; STATISTICAL ESTIMATION; STRUCTURAL EQUATION MODELING; STRUCTURAL EQUATION MODELS;

DYNAMIC PROGRAMMING;

EID: 84919742315     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. O. O. Aalen, K. Roysland, J. M. Gran, and B. Ledergerber. Causality, mediation and time: A dynamic viewpoint. Journal of the Royal Statistical Society: Series A (Statistics in Society), 175(4):831-861, 2012.
2. H. L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science, 209(12):1-45, 1998.
3. P. Büuhlmann, J. Peters, and J. Ernest. CAM: Causal additive models, high-dimensional order search, and penalized regression. Annals of Statistics, 2014. To appear.
4. D. M. Chickering. A transformational characterization of equivalent Bayesian network structures. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, pages 87-98, 1995.
5. D. M. Chickering. Optimal structure identification with greedy search. Journal of Machine Learning Research, 3:507-554, 2002.
6. R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, 1990.
7. T. R. Hughes, M. J. Marton, A. R. Jones, C. J. Roberts, R. Stoughton, C. D. Armour, H. A. Bennett, E. Coffey, H. Dai, Y. D. He, et al. Functional discovery via a compendium of expression profiles. Cell, 102:109-126, 2000.
8. T. Kloks. Treewidth: Computations and Approximations, volume 842. Springer, 1994.
9. D. Koller and N. Friedman. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009.
10. J. H. Korhonen and P. Parviainen. Exact learning of bounded tree-width Bayesian networks. In Artificial Intelligence and Statistics (AISTATS 2013), pages 370-378. JMLR, 2013.
11. S. L. Lauritzen. Graphical Models. Oxford University Press, 1996.
12. P. Loh and M. J. Wainwright. High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity. Annals of Statistics, 40(3):1637-1664, 2012.
13. P. Loh and M. J. Wainwright. Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses. Annals of Statistics, 41(6):3022-3049, 12 2013.
14. N. Meinshausen and P. Büuhlmann. High-dimensional graphs and variable selection with the Lasso. Annals of Statistics, 34:1436-1462, 2006.
15. C. Nowzohour and P. Büuhlmann. Score-based causal learning in additive noise models. arXiv e-prints, April 2014. Available at http://arxiv.org/abs/1311.6359v2.
16. S. Ordyniak and S. Szeider. Algorithms and complexity results for exact Bayesian structure learning. CoRR, abs/1203.3501, 2012.
17. E. Perrier, S. Imoto, and S. Miyano. Finding optimal Bayesian network given a superstructure. Journal of Machine Learning Research, 9(2):2251-2286, 2008.
18. J. Peters and P. Büuhlmann. Identifiability of Gaussian structural equation models with equal error variances. Biometrika, pages 1-10, 2013.
19. P. Ravikumar, M. J. Wainwright, G. Raskutti, and B. Yu. High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence. Electronic Journal of Statistics, 4:935-980, 2011.
20. S. Shimizu, P. O. Hoyer, A. Hyväarinen, and A. Kerminen. A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7:2003-2030, 2006.
21. S. Shimizu, T. Inazumi, Y. Sogawa, A. Hyväarinen, 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, 12:1225-1248, 2011.
22. A. Shojaie and G. Michailidis. Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika, 97(3):519-538, 2010.
23. T. Silander and P. Myllymaki. A simple approach for finding the globally optimal Bayesian network structure. In Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), pages 445-452, Arlington, VA, 2006. AUAI Press.
24. P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search, volume 81. The MIT Press, 2000.
25. D. J. Stekhoven, I. Moraes, G. Sveinbjöornsson, L. Hennig, M. H. Maathuis, and P. Büuhlmann. Causal stability ranking. Bioinformatics, 28(21):2819-2823, 2012.
26. S. van de Geer and P. Büuhlmann. ℓ0-penalized maximum likelihood for sparse directed acyclic graphs. Annals of Statistics, 41(2):536-567, 2013.
27. R. Vershynin. Introduction to the non-asymptotic analysis of random matrices. In Y. C. Eldar and G. Kutyniok, editors, Compressed Sensing: Theory and Applications. Cambridge University Press, 2012.
28. M. Yuan and Y. Lin. Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1):19-35, 2007.