Graphical Modelling in Genetics and Systems Biology

  • Marco Scutari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9521)


Graphical modelling in its modern form was pioneered by Lauritzen and Wermuth [43] and Pearl [56] in the 1980s, and has since found applications in fields as diverse as bioinformatics [28], customer satisfaction surveys [37] and weather forecasts [1]. Genetics and systems biology are unique among these fields in the dimension of the data sets they study, which often contain several thousand variables and only a few tens or hundreds of observations. This raises problems in both computational complexity and the statistical significance of the resulting networks, collectively known as the “curse of dimensionality”. Furthermore, the data themselves are difficult to model correctly due to the limited understanding of the underlying phenomena. In the following, we will illustrate how such challenges affect practical graphical modelling and some possible solutions.


Feature Selection Gene Expression Data Bayesian Network Markov Network Chain Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abramson, B., et al.: Hailfinder: a Bayesian system for forecasting severe weather. Int. J. Forecast. 12(1), 57–71 (1996)CrossRefGoogle Scholar
  2. 2.
    Aliferis, C.F., et al.: Local causal and Markov Blanket induction for causal discovery and feature selection for classification part i: algorithms and empirical evaluation. J. Mach. Learn. Res. 11, 171–234 (2010)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Aliferis, C.F., et al.: Local causal and Markov Blanket induction for causal discovery and feature selection for classification part II: analysis and extensions. J. Mach. Learn. Res. 11, 235–284 (2010)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Astle, W., Balding, D.J.: Population structure and cryptic relatedness in genetic association studies. Stat. Sci. 24(4), 451–471 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Banerjee, O., El Ghaoui, L., d’Aspremont, A.: Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. J. Mach. Learn. Res. 9, 485–516 (2008)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Baragona, R., Battaglia, F., Poli, I.: Evolutionary Statistical Procedures: An Evolutionary Computation Approach to Statistical Procedures Designs and Applications. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley, Chichester (2000)zbMATHGoogle Scholar
  8. 8.
    Breitling, R., et al.: Rank Products: a simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments. FEBS Lett. 573(1–3), 83–92 (2004)CrossRefGoogle Scholar
  9. 9.
    A. J. Butte et al. “Discovering Functional Relationships Between RNA Expression and Chemotherapeutic Susceptibility Using Relevance Networks”. In: PNAS 97 (2000), pp. 12182–12186. 9 Graphical Modelling in Systems Biology 165Google Scholar
  10. 10.
    Cappé, O., Moulines, E., Rydén, T.: Inference in Hidden Markov Models. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  11. 11.
    Castelo, R., Roverato, A.: A robust procedure for Gaussian graphical model search from microarray data with p larger than n. J. Mach. Learn. Res. 7, 2621–2650 (2006)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Castillo, E., Gutiérrez, J.M., Hadi, A.S.: Expert Systems and Probabilistic Network Models. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  13. 13.
    Cheng, J., Druzdel, M.J.: AIS-BN: An adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks. J. Artif. Intell. Res. 13, 155–188 (2000)zbMATHGoogle Scholar
  14. 14.
    Chickering, D.M.: Learning Bayesian Networks is NP-Complete. In: Fisher, D., Lenz, H.J. (eds.) Learning from Data: Artificial Intelligence and Statistics V Part III. LNS, pp. 121–130. Springer-Verlag, Heidelberg (1996)CrossRefGoogle Scholar
  15. 15.
    Cooper, G.F.: The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42(2–3), 393–405 (1990)zbMATHCrossRefGoogle Scholar
  16. 16.
    Cowell, R.G., et al.: Probabilistic Networks and Expert Systems. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  17. 17.
    Cox, D.R., Wermuth, N.: Linear dependencies represented by chain graphs. Stat. Sci. 8(3), 204–218 (1993)zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Fernando, R.L., Habier, D., Kizilkaya, K., Garrick, D.J.: Extension of the Bayesian alphabet for genomic selection. BMC Bioinform. 12(186), 1–12 (2011)Google Scholar
  19. 19.
    Dempster, A.P.: Covariance selection. Biometrics 28, 157–175 (1972)CrossRefGoogle Scholar
  20. 20.
    Duggan, D.J., et al.: Expression profiling using cDNA microarrays. Nature Genetics 21, pp. 10–14 (1999). (Suppl. 1)Google Scholar
  21. 21.
    Edwards, D.I.: Introduction to Graphical Modelling, 2nd edn. Springer, Heidelberg (2000)zbMATHCrossRefGoogle Scholar
  22. 22.
    Falconer, D.S., Mackay, T.F.C.: Introduction to Quantitative Genetics, 4th edn. Longman, Harlow (1996)Google Scholar
  23. 23.
    Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9, 432–441 (2008)zbMATHCrossRefGoogle Scholar
  24. 24.
    Friedman, N.: Inferring cellular networks using probabilistic graphical models. Science 303, 799–805 (2004)CrossRefGoogle Scholar
  25. 25.
    Friedman, N., Geiger, D., Goldszmidt, M.: Bayesian Network Classifiers. Mach. Learn. 29(2–3), 131–163 (1997)zbMATHCrossRefGoogle Scholar
  26. 26.
    Friedman, N., Goldszmidt, M., Wyner, A.: Data analysis with Bayesian networks: a bootstrap approach. In: Laskey, K.B., Prade, H. (eds.) Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence (UAI), pp. 206–215. Morgan Kaufmann, San Francisco (1999)Google Scholar
  27. 27.
    Friedman, N., Koller, D.: Being Bayesian about Bayesian network structure: A Bayesian approach to structure discovery in Bayesian networks. Mach. Learn. 50(1–2), 95–126 (2003)zbMATHCrossRefGoogle Scholar
  28. 28.
    Friedman, N., Linial, M., Nachman, I.: Using Bayesian networks to analyze expression data. J. Comput. Biol. 7, 601–620 (2000)CrossRefGoogle Scholar
  29. 29.
    Friedman, N., Pe’er, D., Nachman, I.: “Learning Bayesian network structure from massive datasets: the “Sparse Candidate” algorithm”. In: Proceedings of 15th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 206–221. Morgan Kaufmann (1999)Google Scholar
  30. 30.
    Friedman, N., et al.: Using Bayesian networks to analyze gene expression data. J. Comput. Biol. 7, 601–620 (2000)CrossRefGoogle Scholar
  31. 31.
    Geiger, D., Heckerman, D.: Learning Gaussian networks. Technical report Available as Technical Report MSR-TR-94-10. Redmond, Washington: Microsoft Research (1994)Google Scholar
  32. 32.
    Hartemink, A.J.: Principled computational methods for the validation and discovery of genetic regulatory networks. PhD thesis. School of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (2001)Google Scholar
  33. 33.
    Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn. 20(3), 197–243 (1995). Available as Technical Report MSR-TR-94-09zbMATHGoogle Scholar
  34. 34.
    Huber, W., et al.: Variance stabilization applied to microarray data calibration and to the quantification of differential expression. Bioinformatics 18(Suppl. 1), S96–S104 (2002)CrossRefGoogle Scholar
  35. 35.
    Imoto, S., et al.: Bootstrap analysis of gene networks based on Bayesian networks and nonparametric regression. Genome Inform. 13, 369–370 (2002)Google Scholar
  36. 36.
    Jonckheere, A.: A Distribution-Free k-Sample test against ordered alternatives. Biometrika 41, 133–145 (1954)zbMATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Kennet, R.S., Perruca, G., Salini, S.: In: Kennet, R.S., Salini, S. (eds.) Modern Analysis of Customer Surveys: with Applications Using R. Wiley, Chichester (2012). (Chap. 11)Google Scholar
  38. 38.
    Koivisto, M., Sood, K.: Exact Bayesian structure discovery in Bayesian networks. J. Mach. Learn. Res. 5, 549–573 (2004)zbMATHMathSciNetGoogle Scholar
  39. 39.
    Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)Google Scholar
  40. 40.
    Koller, D., Sahami, M.: Toward optimal feature selection. In: Proceedings of the 13th International Conference on Machine Learning (ICML), pp. 284–292 (1996)Google Scholar
  41. 41.
    Korb, K., Nicholson, A.: Bayesian Artificial Intelligence, 2nd edn. Chapman and Hall, Boca Raton (2010)Google Scholar
  42. 42.
    Larranaga, P., et al.: Learning Bayesian Networks by Genetic Algorithms: ACase Study in the Prediction of Survival in Malignant Skin Melanoma. In: Keravnou, E., Garbay, C., Baud, R., Wyatt, J. (eds.) AIME 1997. LNCS(LNAI), pp. 261–272. Springer, Heidelberg (1997)Google Scholar
  43. 43.
    Lauritzen, S.L., Wermuth, N.: Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Stat. 17(1), 31–57 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    Lehmann, E.L.: Elements of Large Sample Theory, 3rd edn. Springer, Heidelberg (2004)Google Scholar
  45. 45.
    Lehmann, E.L.: Nonparametrics: Statistical Methods Based on Ranks. Springer, Heidelberg (2006)Google Scholar
  46. 46.
    Lennon, G.G., Lehrach, H.: Hybridization analyses of arrayed cDNA libraries. Trends Genet. 10, 314–317 (1991)CrossRefGoogle Scholar
  47. 47.
    Li, H., Gui, J.: Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic networks. Biostatistics 7, 302–317 (2006)zbMATHCrossRefGoogle Scholar
  48. 48.
    Lipshutz, R.J., et al.: High density synthetic oligonucleotide arrays. Nat. Genet. 21(Suppl. 1), 20–24 (1999)CrossRefGoogle Scholar
  49. 49.
    Meuwissen, T.H.E., Hayes, B.J., Goddard, M.E.: Prediction of totalgenetic value using genome-wide dense marker maps. Genetics 157, 1819–1829 (2001)Google Scholar
  50. 50.
    Morota, G., et al.: An assessment of linkage disequilibrium in Holstein Cattle Using a Bayesian Network. Journal of Animal Breeding and Genetics 129, 474–487 (2012)Google Scholar
  51. 51.
    Mukherjee, S., Speed, T.P.: Network inference using informative priors. PNAS 105, 14313–14318 (2008)CrossRefGoogle Scholar
  52. 52.
    Musella, F.: Learning a Bayesian network from ordinal data. Working Paper 139. Dipartimento di Economia, Università degli Studi “Roma Tre” (2011)Google Scholar
  53. 53.
    Neapolitan, R.E.: Learning Bayesian Networks. Prentice Hall, New York (2003)Google Scholar
  54. 54.
    Park, T., Casella, G.: The Bayesian lasso. J. Am. Stat. Assoc. 103(482), 681–686 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  55. 55.
    Pearl, J.: Causality: Models, Reasoning and Inference, 2nd edn. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  56. 56.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)Google Scholar
  57. 57.
    Pirie, W.: Jonckheere Tests for Ordered Alternatives. In: Encyclopaedia of Statistical Sciences, pp. 315–318. Wiley (1983)Google Scholar
  58. 58.
    Sachs, K., et al.: Causal protein-signaling networks derived from multiparameter single-cell data. Science 308(5721), 523–529 (2005)CrossRefGoogle Scholar
  59. 59.
    Schäfer, J., Strimmer, K.: A Shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat. Appl. Genet. Mol. Biol. 4, 32 (2005)MathSciNetGoogle Scholar
  60. 60.
    Schäfer, J., Strimmer, K.: An Empirical bayes approach to inferring large-scale gene association networks. Bioinformatics 21, 754–764 (2005)CrossRefGoogle Scholar
  61. 61.
    Schuchhardt, J., et al.: Normalization strategies for cDNA microarrays. Nucleic Acids Res. 28, e47 (2000)CrossRefGoogle Scholar
  62. 62.
    Scutari, M., Brogini, A.: Bayesian network structure learning with permutation tests. Commun. Stat. Theory Methods 41(16–17), 3233–3243 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  63. 63.
    Scutari, M., Mackay, I., Balding, D.J.: Improving the efficiency of genomic selection. Stat. Appl. Genet. Mol. Biol. 12(4), 517–527 (2013)MathSciNetGoogle Scholar
  64. 64.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search. MIT Press, Cambridge (2000)Google Scholar
  65. 65.
    Spirtes, P., et al.: Constructing Bayesian network models of gene expression networks from microarray data. In: Proceedings of the Atlantic Symposium on Computational Biology, Genome Information Systems and Technology (2001)Google Scholar
  66. 66.
    Steck, H.: “Learning the Bayesian network structure: Dirichlet prior versus data.” In: Proceedings of the 24th Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI 2008), pp. 511–518 (2008)Google Scholar
  67. 67.
    Steck, H., Jaakkola, T.: On the Dirichlet prior and Bayesian regularization. In: Advances in Neural Information Processing Systems (NIPS), pp. 697–704 (2002)Google Scholar
  68. 68.
    Terpstra, T.J.: The asymptotic normality and consistency of Kendall’s test against trend when the ties are present in one ranking. indagationes mathematicae 14, 327–333 (1952)MathSciNetCrossRefGoogle Scholar
  69. 69.
    Thomas, J.G., et al.: An efficient and robust statistical modeling approach to discover differentially expressed genes using genomic expression profiles. Genome Res. 11, 1227–1236 (2001)CrossRefGoogle Scholar
  70. 70.
    Tsamardinos, I., Aliferis, C.F., Statnikov, A.: “Algorithms for large scale Markov blanket discovery”. In: Proceedings of the 16th International Florida Artificial Intelligence Research Society Conference, pp. 376–381 (2003)Google Scholar
  71. 71.
    Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max-min hill-climbing Bayesian network structure learning algorithm. Mach. Learn. 65(1), 31–78 (2006)CrossRefGoogle Scholar
  72. 72.
    Whittaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley, New York (1990)zbMATHGoogle Scholar
  73. 73.
    Yeung, K.Y., et al.: Model-based clustering and data transformations for gene expression data. Bioinformatics 17(10), 977–987 (2001)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of OxfordOxfordUK

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