Score-based causal learning in additive noise models

Statistics

Volumn 50, Issue 3, 2016, Pages 471-485

  Nowzohour, Christopher ^a   Bühlmann, Peter ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

causal inference; hidden variables; latent variables; path diagrams; structural equation models; structure learning

Indexed keywords

EID: 84937777714     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331888.2015.1060237     Document Type: Article

References (32)

1. J.Pearl. Causality. New York: Cambridge University Press; 2000.
2. P.Spirtes, C.Glymour, R.Scheines. Causation, prediction, and search. New York: Springer Verlag; 1993.
3. T.S.Verma, J.Pearl, Equivalence and synthesis of causal models. Paper presented at the 6th Conference on Uncertainty in Artificial Intelligence (UAI). 1991 July 27–29; Cambridge, MA, USA. p. 220–227.
4. A.Statnikov, M.Henaff, N.I.Lytkin, C.F.Aliferis. New methods for separating causes from effects in genomics data. BMC Genomics. 2012;13 (Suppl. 8):S22.
5. D.J.Stekhoven, I.Moraes, G.Sveinbjornsson, L.Hennig, M.H.Maathuis, P.Bühlmann. Causal stability ranking. Bioinformatics. 2012;28:2819–2823. doi: 10.1093/bioinformatics/bts523
6. J.D.Ramsey, S.J.Hansen, C.Hanson, Y.O.Halchenko, R.A.Poldrack, C.Glymour. Six problems for causal inference from fMRI. NeuroImage. 2010;49:1545–1558. doi: 10.1016/j.neuroimage.2009.08.065
7. K.A.Bollen. Structural equations with latent variables. New York: Wiley; 1989.
8. P.O.Hoyer, D.Janzing, J.Mooji, J.Peters, B.Schölkopf, Nonlinear causal discovery with additive noise models. In: Koller D, Schuurmans D, Bengio Y, Bottou L, editors. Advances in neural information processing systems (NIPS) Vol. 21, 2009. p. 689–696.
9. J.Peters, P.Bühlmann. Identifiability of Gaussian structural equation models with equal error variances. Biometrika. 2014;101:219–228. doi: 10.1093/biomet/ast043
10. J.Peters, J.Mooji, D.Janzing, B.Schölkopf, Identifiability of causal graphs using functional models. Paper presented at the 27th Conference on Uncertainty in Artificial Intelligence (UAI). 2011 July 14–17; Barcelona, Spain. p. 589–598.
11. S.Shimizu, P.O.Hoyer, A.Hyvärinen, A.Kerminen. A linear non-Gaussian acyclic model for causal discovery. J Mach Learn Res. 2006;7:2003–2030.
12. K.Zhang, A.Hyvärinen, On the identifiability of the post-nonlinear causal model. Paper presented at the 25th Conference on Uncertainty in Artificial Intelligence (UAI). 2009 June 18–21; Montreal, QC, Canada. p. 647–655.
13. J.Mooij, D.Janzing, J.Peters, B.Schölkopf, Regression by dependence minimization and its application to causal inference. Proceedings of the 26th International Conference on Machine Learning (ICML), 2009 June 14–18; Montreal, Canada. p. 745–752.
14. D.M.Chickering. Optimal structure identification with greedy search. J Mach Learn Res. 2002;3:507–554.
15. D.Koller, N.Friedman. Probabilistic graphical models. Cambridge: The MIT Press; 2009.
16. S.Imoto, T.Goto, S.Miyano, Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. In: Pacific Symposium on Biocomputing. 2002 January 3–7; Lihue, Hawaii. p. 175–186.
17. A.Hyvärinen, S.M.Smith. Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. J Mach Learn Res. 2013;14:111–152.
18. P.Bühlmann, J.Peters, J.Ernest. CAM: Causal additive models, high-dimensional order search and penalized regression. Ann Stat. 2014;42:2526–2556. doi: 10.1214/14-AOS1260
19. S.Kpotufe, E.Sgouritsa, D.Janzig, B.Schölkopf, Consistency of causal inference under the additive noise model. Proceedings of The 31st International Conference on Machine Learning (ICML). 2014 June 21–26; Beijing, China. p. 478–486.
20. S.L.Lauritzen. Graphical models. Oxford: Oxford University Press; 1996.
21. H.Triebel. Theory of function spaces. New York: Springer; 1983.
22. T.Hastie, R.Tibshirani. Generalized additive models. Stat Sci. 1986;1:297–318. doi: 10.1214/ss/1177013604
23. W.S.Cleveland. Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc. 1979;74:829–836. doi: 10.1080/01621459.1979.10481038
24. C.Kooperberg, C.J.Stone. A study of logspline density estimation. Comput Stat Data Anal. 1991;12:327–347. doi: 10.1016/0167-9473(91)90115-I
25. K.Emancipator, M.H.Kroll. A quantitative measure of nonlinearity. Clin. Chem. 1993;39:766–772.
26. J.Mooji, D.Janzing, Distinguishing between cause and effect. In: Journal of Machine Learning Workshop and Conference Proceedings, 2010;6:147–156.
27. K.Zhang, A.Hyvärinen, Distinguishing causes from effects using nonlinear acyclic causal models. In: Journal of Machine Learning Workshop and Conference Proceedings 2010;6:157–164.
28. D.Janzing, J.Mooji, K.Zhang, J.Lemeire, J.Zscheischler, P.Daniusis, B.Steudel, B.Schölkopf. Information-geometric approach to inferring causal directions. Artificial Intelligence. 2012;182–183:1–31. doi: 10.1016/j.artint.2012.01.002
29. S.van de Geer. Empirical processes in M-Estimation. Cambridge (UK): Cambridge University Press; 2000.
30. A.W.van der Vaart, J.A.Wellner. Weak convergence and empirical processes: with applications to statistics. New York: Springer; 1996.
31. P.Bühlmann, S.van de Geer. Statistics for high-dimensional data. Berlin: Springer; 2011.
32. R.Nickl, B.M.Pötscher. Bracketing metric entropy rates and empirical central limit theorems for function classes of besov- and sobolev-type. J Theor Probab. 2007;20:177–199. doi: 10.1007/s10959-007-0058-1