Skip to main content
Log in

An Overview of Recent Advancements in Causal Studies

  • Original Paper
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

In causal study we are interested in finding the graphical structure in the form of directed acyclic graphs (DAGs). These DAGs describe the directions and connection strength to connecting variables represented by nodes. In this regard, various methods have been developed to estimate the appropriate structure of the causal model and to explain a fair number of its features. Our review aims to provide a complete and systematic analysis of selected articles from past few decades, having powerful methods to infer the area of study. In this article, we categorized all selected articles in three groups, on the basis of techniques these used to construct the causal model. To provide a full comparative study under categories of probabilistic, statistical and algebraic approaches, we discussed underlying difficulties, limitations, merits and disadvantages in applying these techniques. The reader will find it helpful to choose and use the appropriate method for a better implication.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Bach FR, Jordan MI (2002) Kernel independent component analysis. J Mach Learn Res 3:1–48

    MathSciNet  MATH  Google Scholar 

  2. Beal MJ, Ghahramani Z (2004) Variational Bayesian learning of directed graphical models with hidden variables. Bayesian Anal 1:1–44

    MathSciNet  MATH  Google Scholar 

  3. Bollen KA (1989) Structural equations with latent variables. Wiley, New York

    Book  MATH  Google Scholar 

  4. Borgelt C (2010) A conditional independence algorithm for learning undirected graphical models. J Comput Syst Sci 76:21–33

    Article  MathSciNet  MATH  Google Scholar 

  5. Cichocki A, Amari SI (2002) Adaprive blind signal and image processing. Wiley, New York

    Book  Google Scholar 

  6. Chwialkowski K, Gretton A (2014) A kernel independence test for random processes. In: Proceedings of the 31st international conference on machine learning. arXiv:1402.4501

  7. Eliden G, Nachman I, Friedman N (2007) “Ideal Parent” structure learning for continuous variable Bayesian networks. J Mach Learn Res 8:1799–1833

    MathSciNet  MATH  Google Scholar 

  8. Freiedman N, Koller D (2003) Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Mach Learn 50:95–125

    Article  MATH  Google Scholar 

  9. Fukumizu K, Bach FR, Gretton A (2007) Statistical consistency of kernel canonical correlation analysis. J Mach Learn Res 8:361–383

    MathSciNet  MATH  Google Scholar 

  10. Geng Z, He YB, Wang XL, Zhao Q (2003) Bayesian method for learning graphical models with incompletely categorical data. Comput Stat Data Anal 44:175–192

    Article  MathSciNet  MATH  Google Scholar 

  11. Gretton A, Bousquet O, Smol AJ, Schölkopf B (2005) Measuring statistical dependence with Hilbert–Schmidt norms. In: Algorithmic learning theory: 16th international conference (ALT2005), vol 3734, pp 63–77

  12. Gretton A, Herbrich R, Smola A (2003) The kernel mutual information. In: Proceedings of IEEE internaltional conference on acoustics, speech and signal processing (ICASSP 2003), pp 880–883

  13. Gretton A, Herbrich R, Smola A, Bousquet O, Schölkopf B (2005) Kernel methods for measuring independence. J Mach Learn Res 6:2075–2129

    MathSciNet  MATH  Google Scholar 

  14. Gretton A, Smola A, Bousquet O, Herbrich R, Belitski A, Augath M, Murayama Y, Pauls J, Schölkopf B, Logothetis N (2005) Kernel constrained covariance for dependence measurement. In AISTATS 10, pp 112–119

  15. Gretton A, Fukumizu K, Teo CH, Song L, Schölkopf B, Smola AJ, Koller D, Singer Y, Roweis S (2007) A kernel statistical test of independence. In: Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007), Curran, pp 585–592

  16. He YB, Geng Z (2008) Active learning of causal networks with intervention experiments and optimal designs. J Mach Learn Res 9:2523–2547

    MathSciNet  MATH  Google Scholar 

  17. Hofmann T, Schölkopf B, Smola AJ (2008) Kernel methods in machine learning. Ann Stat 36(3):1171–1220. doi:10.1214/009053607000000677

    Article  MathSciNet  MATH  Google Scholar 

  18. Hoyer PO, Janzing D, Mooij J, Peters J, Schölkopf B (2009) Nonlinear causal discovery with additive noise models. In: Koller D, Schuurmans D, Bengio Y, Bottou L (eds) Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008, Red Hook, NY, Curran, pp 689–696

  19. Hyvärinen A, Smith SM (2013) Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. J Mach Learn Res 14:111–152

    MathSciNet  MATH  Google Scholar 

  20. Janzing D, Mooij J, Zhang K, Lemeire J, Zscheischler J, Daniuis P, Steudel B, Schölkopf B (2012) Information-geometric approach to inferring causal directions. Artif Intell 182–183:1–31

    Article  MathSciNet  MATH  Google Scholar 

  21. Gilks WR, Richardson S, Spiegelhalter DJ (1996) Introducing markov chain monte carlo. Markov Chain Monte Carlo Pract 1:19

    MATH  Google Scholar 

  22. Pearl J (1998) Probabilistic reasoning in intelligent systems. Morgan Kaufmann, San Francisco. ISBN 0-934613-73-7

  23. Pearl J (2000) Causality: models, reasoning, and inference, 2nd edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  24. Pearl J (2009) Causal inference in statistics: an overview. Stat Surv 3:96–146. ISSN: 1935–7516. DOI:10.1214/09-SS057

  25. Pellet JP, Elisseeff A (2008) Using Markov blankets for causal structure learning. J Mach Learn Res 9:1295–1342

    MathSciNet  MATH  Google Scholar 

  26. Petrović L, Dimitrijević S (2011) Invariance of statistical causality under convergence. Stat Probab Lett 81(9):1445–1448

    Article  MathSciNet  MATH  Google Scholar 

  27. Roy S, Lane T, Washburne MW (2009) Learning structurally consistent undirected probabilistic graphical models. In: Proceedings of the 26th annual international conference on machine learning, pp 905–912. ACM

  28. Shimizu S, Hoyer PO, Hyvärinen A, Kerminen A (2006) A linear non-Gaussian acyclic model for causal discovery. J Mach Learn Res 7:2003–2030

    MathSciNet  MATH  Google Scholar 

  29. Shimizu S, Inazumi T, Sogawa Y, Hyvärinen A, Kawahara Y, Washio T, Hoyer PO, Bollen K (2011) DirectLiNGAM: a direct method for learning a linear non-Gaussian structural equation model. J Mach Learn Res 12:1225–1248

    MathSciNet  MATH  Google Scholar 

  30. Shpitser I, Pearl J (2008) Complete identification methods for the causal hierarchy. J Mach Learn Res 9:1941–1979

    MathSciNet  MATH  Google Scholar 

  31. Song L, Smola A, Gretton A, Bedo J, Borgwardt K (2012) Feature selection via dependence maximization. J Mach Learn Res 13(1):1393–1434

    MathSciNet  MATH  Google Scholar 

  32. Spirtes P, Glymour C, Scheines R (1993) Causation, prediction, and search, 2nd edn. Springer, New york

    Book  MATH  Google Scholar 

  33. Sun X, Janzing D, Schölkopf B (2006) Causal inference by choosing graphs with most plausible Markov kernels. In: Proceeding of the 9th international symposium on artificial intelligence and mathematics, Fort Lauderdale, Florida

  34. Sun X, Janzing D, Schölkopf B, Fukumizu K (2007) A kernel-based causal learning algorithm. In Proceedings of the 24th international conference on Machine learning, pp 855–862

  35. Uhler C, Raskutti G, Bühlmann P, Yu B (2013) Geometry of the faithfulness assumption in causal inference. Ann Stat 41(2):436–463. doi:10.1214/12-AOS1080

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhang J (2008) Causal reasoning with ancestral graphs. J Mach Learn Res 9:1437–1474

    MathSciNet  MATH  Google Scholar 

  37. Zhang K, Hyvärinen A (2008) Distinguishing causes from effects using nonlinear acyclic causal models. In: Journal of machine learning research, workshop and conference proceedings (NIPS 2008 causality workshop), vol. 6, pp 157–164

  38. Zhang K, Hyvärinen A (2009) On the identifiability of the post-nonlinear causal model. In: Proceedings of the twenty-fifth conference on uncertainty in artificial intelligence, pp 647–655. AUAI Press

  39. Zhang X, Song L, Gretton A, Smola AJ (2009) Kernel measures of independence for non-iid data. Adv Neural Inf Process Syst 21:1937–1944

    Google Scholar 

  40. Zhang K, Peters J, Janzing D, Schölkopf B (2012) Kernel-based conditional independence test and application in causal discovery. arXiv:1202.3775

  41. Zwald L, Bousquet O, Blanchard G (2004) Statistical properties of kernel principal component analysis. In: Proceedings of 17th annual conference on learning theory (COLT 2004), pp 594–608

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pramod Kumar Parida.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parida, P.K., Marwala, T. & Chakraverty, S. An Overview of Recent Advancements in Causal Studies. Arch Computat Methods Eng 24, 319–335 (2017). https://doi.org/10.1007/s11831-016-9168-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-016-9168-1

Keywords

Navigation