Asymptotical Lower Limits on Required Number of Examples for Learning Boolean Networks

  • Osman Abul
  • Reda Alhajj
  • Faruk Polat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)


This paper studies the asymptotical lower limits on the required number of samples for identifying Boolean Networks, which is given as Ω(logn) in the literature for fully random samples. It has also been found that O(logn) samples are sufficient with high probability. Our main motivation is to provide tight lower asymptotical limits for samples obtained from time series experiments. Using the results from the literature on random boolean networks, lower limits on the required number of samples from time series experiments for various cases are analytically derived using information theoretic approach.


Bayesian Network Boolean Function Require Number Genetic Network Boolean Network 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abul, O.: Controlling discrete genetic regulatory networks. PhD Thesis, Middle East Technical University (January 2005)Google Scholar
  2. 2.
    Akutsu, T., Kuhara, S., Maruyama, O., Miyano, S.: Identification of genetic networks by strategic gene disruptions and gene overexpressions under a boolean model. Theoretical Computer Science 298, 235–251 (2003)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Akutsu, T., Kuhara, S., Miyano, S.: Identification of genetic networks from a small number of gene expression patterns under the boolean network model. In: Proc. of Pacific Symposium on Biocomputing, pp. 17–28 (1999)Google Scholar
  4. 4.
    Akutsu, T., Miyano, S., Kuhara, S.: Algorithms for identifying boolean networks and related biological networks based on matrix multiplication and fingerprint function. In: Proc. of Research in Computational Molecular Biology, pp. 8–14 (2000)Google Scholar
  5. 5.
    Aldana, M.: Boolean dynamics of networks with scale-free topology. Physica D (2003)Google Scholar
  6. 6.
    Chen, T., He, H.L., Church, G.M.: Modelling gene expression with differential equations. In: Proc. of Pacific Symposium on Biocomputing, pp. 29–40 (1999)Google Scholar
  7. 7.
    D’haesseleer, P., Liang, S., Somogyi, R.: Genetic network inference: from co-expression clustering to reverse engineering. Bioinformatics 16(8), 707–726 (2000)CrossRefGoogle Scholar
  8. 8.
    Friedman, N., Linial, M., Nachman, I., Peer, D.: Using bayesian networks to analyze expression data. Computational Biology 7, 601–620 (2000)CrossRefGoogle Scholar
  9. 9.
    Imoto, S., Goto, T., Miyano, S.: Estimation of genetic networks and functional structures between genes by using bayesian networks and nonparametric regression. In: Proc. of Pacific Symposium on Biocomputing, pp. 175–186 (2002)Google Scholar
  10. 10.
    Kauffman, S.A.: The origins of order: Self organization and selection in evolution. Oxford University Press, New York (1993)Google Scholar
  11. 11.
    Kim, S., Li, H., Dougherty, E.R., Cao, N., Chen, Y., Bittner, M., Suh, E.B.: Can markov chain models mimic biological regulation. Biological Systems 10(4), 337–357 (2002)MATHCrossRefGoogle Scholar
  12. 12.
    Lahdesmaki, H., Shmulevich, I., Yli-Harja, O.: On learning gene regulatory networks under the boolean network model. Machine Learning 52, 147–167 (2003)CrossRefGoogle Scholar
  13. 13.
    Liang, S., Fuhrman, S., Somogyi, R.: REVEAL: A general reverse engineering algorithm for inference of genetic network architectures. In: Proc. of Pacific Symposium on Biocomputing, pp. 18–29 (1998)Google Scholar
  14. 14.
    Matsuno, H., Doi, A., Nagasaki, M., Miyano, S.: Hybrid petri net representation of gene regulatory network. In: Proc. of Pacific Symposium on Biocomputing, pp. 341–352 (2000)Google Scholar
  15. 15.
    Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.: Probabilistic boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261–274 (2002)CrossRefGoogle Scholar
  16. 16.
    Shmulevich, I., Dougherty, E.R., Zhang, W.: Control of stationary behavior in probabilistic boolean networks by means of structural intervention. Biological Systems 10, 431–446 (2002)MATHCrossRefGoogle Scholar
  17. 17.
    Shmulevich, I., Yli-Harja, O., Astola, J.: Inference of genetic regulatory networks under the best-fit extension paradigm. Computational and Statistical Approaches to Genomics (2002)Google Scholar
  18. 18.
    Somogyvari, Z., Payrits, S.: Length of state cycles of random boolean networks: ananalytic study. J. Phys. A 33, 6699–6706 (2000)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Weaver, D.C., Workman, C.T., Stormo, G.D.: Modeling regulatory networks with weight matrices. In: Proc. of Pacific Symposium on Biocomputing (1999)Google Scholar
  20. 20.
    Wuensche, A.: Genomic regulation modeled as a network with basins of attaction. In: Proc. of Pacific Symposium on Biocomputing, pp. 89–102 (1998)Google Scholar
  21. 21.
    Yoo, C., Thorsson, V., Cooper, G.F.: Discovery of cuasal relationships in a gene regulation pathway from a mixture of experimental and observational DNA microarray data. In: Proc. of Pacific Symposium on Biocomputing, pp. 498–509 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Osman Abul
    • 1
  • Reda Alhajj
    • 2
    • 3
  • Faruk Polat
    • 4
  1. 1.Dept of Cancer Research and Molecular MedicineNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Dept of Computer ScienceUniversity of CalgaryCalgary, AlbertaCanada
  3. 3.Dept of Computer ScienceGlobal UniversityBeirutLebanon
  4. 4.Dept of Computer EngineeringMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations