Learning high-dimensional directed acyclic graphs with latent and selection variables

Annals of Statistics

Volumn 40, Issue 1, 2012, Pages 294-321

  Colombo, Diego ^a   Maathuis, Marloes H ^a   Kalisch, Markus ^a   Richardson, Thomas S ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Causal structure learning; Consistency; FCI algorithm; High dimensionality; Maximal ancestral graphs (MAGs); Partial ancestral graphs (PAGs); RFCI algorithm; Sparsity

Indexed keywords

EID: 84867677322     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS940     Document Type: Article

References (25)

1. AHO, A., HOPCROFT, J. and ULLMAN, J. D. (1974). The Design and Analysis of Computer Algorithms. Addison-Wesley, Boston, MA.
2. ALI, R. A., RICHARDSON, T. S. and SPIRTES, P. (2009). Markov equivalence for ancestral graphs. Ann. Statist. 37 2808-2837. MR25414488
3. ANDERSSON, S. A., MADIGAN, D. and PERLMAN, M. D. (1997). A characterization of Markov equivalence classes for acyclic digraphs. Ann. Statist. 25 505-541. MR14393122
4. CHICKERING, D. M. (2002). Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2 445-498. MR19294155
5. COLOMBO, D., MAATHUIS, M. H., KALISCH, M. and RICHARDSON, T. S. (2012). Supplement to "Learning high-dimensional directed acyclic graphs with latent and selection variables." DOI:10.1214/11-AOS940SUPP.
6. COOPER, G. (1995). Causal discovery from data in the presence of selection bias. In Preliminary Papers of the Fifth International Workshop on Artificial Intelligence and Statistics (D. Fisher, ed.) 140-150.
7. DAWID, A. P. (1980). Conditional independence for statistical operations. Ann. Statist. 8 598- 617. MR05687233
8. KALISCH, M. and BÜHLMANN, P. (2007). Estimating high-dimensional directed acyclic graphs with the PC-algorithm. J. Mach. Learn. Res. 8 613-636.
9. KALISCH, M., MÄCHLER, M., COLOMBO, D., MAATHUIS, M. H. and BÜHLMANN, P. (2012). Causal inference using graphical models with the R package pcalg. J. Statist. Software. To appear.
10. MAATHUIS, M. H., COLOMBO, D., KALISCH, M. and BÜHLMANN, P. (2010). Predicting causal effects in large-scale systems from observational data. Nat. Methods 7 247-248.
11. MAATHUIS, M. H., KALISCH, M. and BÜHLMANN, P. (2009). Estimating high-dimensional intervention effects from observational data. Ann. Statist. 37 3133-3164. MR25495555
12. MEINSHAUSEN, N. and BÜHLMANN, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436-1462. MR22783633
13. PEARL, J. (2000). Causality. Models, Reasoning, and Inference. Cambridge Univ. Press, Cambridge. MR17447733
14. PEARL, J. (2009). Causal inference in statistics: An overview. Stat. Surv. 3 96-146. MR25452911
15. RAMSEY, J., ZHANG, J. and SPIRTES, P. (2006). Adjacency-faithfulness and conservative causal inference. In Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence. AUAI Press, Arlington, VA.
16. RICHARDSON, T. and SPIRTES, P. (2002). Ancestral graph Markov models. Ann. Statist. 30 962-1030. MR19261666
17. RICHARDSON, T. S. and SPIRTES, P. (2003). Causal inference via ancestral graph models. In Highly Structured Stochastic Systems. Oxford Statistical Science Series 27 83-113. Oxford Univ. Press, Oxford. MR20824077
18. ROBINS, J. M., HERNÁN, M. A. and BRUMBACK, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11 550-560.
19. SPIRTES, P. (2001). An anytime algorithm for causal inference. In Proc. of the Eighth International Workshop on Artificial Intelligence and Statistics 213-221. Morgan Kaufmann, San Francisco.
20. SPIRTES, P., GLYMOUR, C. and SCHEINES, R. (2000). Causation, Prediction, and Search, 2nd ed. MIT Press, Cambridge, MA. MR18156755
21. SPIRTES, P., MEEK, C. and RICHARDSON, T. (1999). An algorithm for causal inference in the presence of latent variables and selection bias. In Computation, Causation, and Discovery 211-252. AAAI Press, Menlo Park, CA. MR16899722
22. VERMA, T. and PEARL, J. (1990). Equivalence and synthesis of causal models. In Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence 255-270. Elsevier, New York.
23. ZHANG, J. (2008). Causal reasoning with ancestral graphs. J. Mach. Learn. Res. 9 1437-1474. MR24260488
24. ZHANG, J. (2008). On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence 172 1873-1896. MR24597933
25. ZHAO, P. and YU, B. (2006). On model selection consistency of Lasso. J. Mach. Learn. Res. 7 2541-2563. MR22744499