A linear non-gaussian acyclic model for causal discovery

Journal of Machine Learning Research

Volumn 7, Issue , 2006, Pages 2003-2030

  Shimizu, Shohei ^a,b   Hoyer, Patrik O ^a   Hyvärinen, Aapo ^a   Kerminen, Antti ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Causal discovery; Directed acyclic graph; Independent component analysis; Non experimental data; Non Gaussianity

Indexed keywords

DATA ACQUISITION; GRAPH THEORY; INDEPENDENT COMPONENT ANALYSIS; MATHEMATICAL MODELS; STATISTICAL METHODS;

CAUSAL DISCOVERY; DIRECTED ACYCLIC GRAPH; NON-EXPERIMENTAL DATA; NON-GAUSSIANITY;

LINEAR SYSTEMS;

EID: 33749326177     PISSN: 15337928     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. Y. Benjamini and Y. Hochberg. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57:289-300, 1995.
2. K. A. Bollen. Structural Equations with Latent Variables. John Wiley & Sons, 1989.
3. G. E. P. Box and G. M. Jenkins. Time Series Analysis: forecasting and control. Holden-Day, Oakland, California, USA, revised edition, 1976.
4. P. J. Brockwell and R. A. Davis. Time Series: Theory and Methods. Springer-Verlag, New York, USA, 1987.
5. M. W. Browne. Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 9:665-672, 1984.
6. R. E. Burkard and E. Cela. Linear assignment problems and extensions. In P. M. Pardalos and D. Z. Du, editors, Handbook of Combinatorial Optimization - Supplement Volume A, pages 75-149. Kluwer, 1999.
7. J.-F. Cardoso and B. H. Laheld. Equivariant adaptive source separation. IEEE Trans. on Signal Processing, 44:3017-3030, 1996.
8. J.-F. Cardoso and A. Souloumiac. Blind beamforming for non Gaussian signals. IEE Proceedings-F, 140(6):362-370, 1993.
9. P. Comon. Independent component analysis - a new concept? Signal Processing, 36:287-314, 1994.
10. Y. Dodge and V. Rousson. On asymptotic properties of the correlation coefficient in the regression setting. The American Statistician, 55(1):51-54, 2001.
11. B. Efron and R. Tibshirani. An Introduction to the Bootstrap. Chapman & Hall, New York, 1993.
12. D. Geiger and D. Heckerman. Learning ganssian networks. In Proceedings of the 10th Annual Conference on Uncertainty in Artificial Intelligence (UAI-94), pages 235-243, 1994.
13. V. P. Godambe. Estimating functions. Oxford University Press, New York, 1991.
14. J. Himberg, A. Hyvärinen, and F. Esposito. Validating the independent components of neuroimaging time-series via clustering and visualization. Neuroimage, 22:1214-1222, 2004.
15. Y. Hochberg. A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 4: 800-802, 1988.
16. Y. Hochberg and A. C. Tamhane. Multiple comparison procedures. John Wiley & Sons, New York, 1987.
17. S. Holm. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6:65-70, 1979.
18. P. O. Hoyer, S. Shimizu, A. Hyvärinen, Y. Kano, and A. J. Kerminen. New permutation algorithms for causal discovery using ICA. In Proceedings of International Conference on Independent Component Analysis and Blind Signal Separation, Charleston, SC, USA, pages 115-122, 2006a.
19. P. O. Hoyer, S. Shimizu, and A. J. Kerminen. Estimation of linear, non gaussian causal models in the presence of confounding latent variables. In Proc. the third European Workshop on Probabilistic Graphical Models (PGM2006), 2006b. In press.
20. L. Hu, P. M. Bentler, and Y. Kano. Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112:351-362, 1992.
21. R. J. Hyndman. Time series data library, 2005. URL http: //www-personal.buseco.monash.edu.au/~hyndman/TSDL/. [June 2005].
22. A. Hyvärinen. One-unit contrast functions for independent component analysis: A statistical analysis. In Neural Networks for Signal Processing VII (Proceedings of IEEE Workshop on Neural Networks for Signal Processing), pages 388-397, 1997.
23. A. Hyvärinen. Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. on Neural Networks, 10(3):626-634, 1999.
24. A. Hyvärinen, J. Karhunen, and E. Oja. Independent Component Analysis. Wiley Interscience, 2001.
25. M. Kawanabe and K. R. Müller. Estimating functions for blind separation when sources have variance dependencies. Journal of Machine Learning Research, 6:453-482, 2005.
26. National Statistics, 2005. URL http://www.statistics.gov.uk/.[June2005].
27. J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2000.
28. D. T. Pham and P. Garrat. Blind separation of mixture of independent sources through a quasimaximum likelihood approach. Signal Processing, 45:1457-1482, 1997.
29. S. Shimizu, A. Hyvärinen, P. O. Hoyer, and Y. Kano. Finding a causal ordering via independent component analysis. Computational Statistics & Data Analysis, 50(11):3278-3293, 2006a.
30. S. Shimizu, A. Hyvärinen, Y. Kano, and P. O. Hoyer. Discovery of non gaussian linear causal models using ICA. In Proc. the 21st Conference on Uncertainty in Artificial Intelligence (UAI2005), pages 526-533, 2005.
31. S. Shimizu, A. Hyvärinen, Y. Kano, P. O. Hoyer, and A. J. Kerminen. Testing significance of mixing and demixing coefficients in ICA. In Proceedings of International Conference on Independent Component Analysis and Blind Signal Separation, Charleston, SC, USA, pages 901-908, 2006b.
32. S. Shimizu and Y. Kano. Use of non-normality in structural equation modeling: Application to direction of causation. Journal of Statistical Planning and Inference, 2006. In press.
33. R. J. Simes. An improved Bonferroni procedure for multiple tests of significance. Biometrika, 73: 751-754, 1986.
34. P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search, 2nd ed. MIT Press, 2000.
35. Statistical Software Information, 2005. URL http://www-unix.oit.umass. edu/~statdata/.[June 2005].
36. P. Tichavský, Z. Koldovský, and E. Oja. Performance analysis of the FastICA algorithm and Cram̀r-Rao bounds for linear independent component analysis. IEEE Trans. on Signal Processing, 54(4): 1189-1203, 2006.
37. K-H. Yuan and P. M. Bentler. Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92(438):767-774, 1997.