A Statistic Criterion for Reducing Indeterminacy in Linear Causal Modeling

Gianluca Bontempi

Abstract

Inferring causal relationships from observational data is still an open challenge in machine learning. State-of-the-art approaches often rely on constraint-based algorithms which detect v-structures in triplets of nodes in order to orient arcs. These algorithms are destined to fail when confronted with completely connected triplets. This paper proposes a criterion to deal with arc orientation also in presence of completely linearly connected triplets. This criterion is then used in a Relevance-Causal (RC) algorithm, which combines the original causal criterion with a relevance measure, to infer causal dependencies from observational data. A set of simulated experiments on the inference of the causal structure of linear networks shows the effectiveness of the proposed approach.

References

  1. Aliferis, C., Tsamardinos, I., and Statnikov, A. (2003). Causal explorer: A probabilistic network learning toolkit for biomedical discovery. In The 2003 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS 7803).
  2. Anderson, R. and Vastage, G. (2004). Causal modeling alternatives in operations research: overview and application. Eurpean Journal of Operational Research, 156:92-109.
  3. Bollen, K. (1989). Structural equations with latent variables. John Wiley and Sons.
  4. Bontempi, G., Haibe-Kains, B., Desmedt, C., Sotiriou, C., and Quackenbush, J. (2011). Multiple-input multipleoutput causal strategies for gene selection. BMC bioinformatics, 12(1):458.
  5. Bontempi, G. and Meyer, P. (2010). Causal filter selection in microarray data. In Proceeding of the ICML2010 conference.
  6. Bowden, R. and Turkington, D. (1984). Instrumental Variables. Cambridge University Press.
  7. Brown, G. (2009). A new perspective for information theoretic feature selection. In Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS).
  8. Graybill, F. (1976). Theory and Application of the Linear Model. Duxbury Press.
  9. Guyon, I., Aliferis, C., and Elisseeff, A. (2007). Computational Methods of Feature Selection, chapter Causal Feature Selection, pages 63-86. Chapman and Hall.
  10. Hershberger, S. (2006). Structural equation modeling: a second course, chapter The problems of equivalent structural models, pages 13-41. Springer.
  11. Janzing, D., Hoyer, P. O., and Scholkopf, B. (2010). Telling cause from effect based on high-dimensional observations. In Proceeding of the ICML2010 conference.
  12. Janzing, D., Sgouritsa, E., Stegle, O., Peters, J., and Scholkopf, B. (2011). Detecting low-complexity unobserved causes. In Conference on Uncertainty in Artificial Intelligence (UAI2011).
  13. Koller, D. and Friedman, N. (2009). Probabilistic graphical models. The MIT Press.
  14. Mulaik, S. (2009). Linear Causal Modelling with Structural Equations. CRC Press.
  15. Peng, H., Long, F., and Ding, C. (2005). Feature selection based on mutual information: Criteria of max-dependency,max-relevance, and minredundancy. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(8):1226-1238.
  16. Spirtes, P., Glymour, C., and Scheines, R. (2000). Causation, Prediction and Search. Springer Verlag, Berlin.
  17. Stelzl, I. (1986). Changing a causal hypothesis without changing the fit: Some rules for generating equivalent path models. Multivariate Behavioral Research, 21:309?331.
  18. Tsamardinos, I., Aliferis, C., and Statnikov, A. (2003). Algorithms for large scale markov blanket discovery. In Proceedings of the 16th International FLAIRS Conference (FLAIRS 2003).
  19. Watkinson, J., Liang, K., Wang, X., Zheng, T., and Anastassiou, D. (2009). Inference of regulatory gene interactions from expression data using three-way mutual information. Annals of N.Y. Academy of Sciences, 1158:302-313.
  20. b1 0
Download


Paper Citation


in Harvard Style

Bontempi G. (2013). A Statistic Criterion for Reducing Indeterminacy in Linear Causal Modeling . In Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-8565-41-9, pages 159-166. DOI: 10.5220/0004254301590166


in Bibtex Style

@conference{icpram13,
author={Gianluca Bontempi},
title={A Statistic Criterion for Reducing Indeterminacy in Linear Causal Modeling},
booktitle={Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},
year={2013},
pages={159-166},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004254301590166},
isbn={978-989-8565-41-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - A Statistic Criterion for Reducing Indeterminacy in Linear Causal Modeling
SN - 978-989-8565-41-9
AU - Bontempi G.
PY - 2013
SP - 159
EP - 166
DO - 10.5220/0004254301590166