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ISaaC: Identifying Structural Relations in Biological Data with Copula-Based Kernel Dependency Measures

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Bioinformatics and Biomedical Engineering (IWBBIO 2018)

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Abstract

The goal of this paper is to develop a novel statistical framework for inferring dependence between distributions of variables in omics data. We propose the concept of building a dependence network using a copula-based kernel dependency measures to reconstruct the underlying association network between the distributions. ISaaC is utilized for reverse-engineering gene regulatory networks and is competitive with several state-of-the-art gene regulatory inferrence methods on DREAM3 and DREAM4 Challenge datasets. An open-source implementation of ISaaC is available at https://bitbucket.org/HossamAlmeer/isaac/.

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References

  1. Bach, F.R., Jordan, M.I.: Kernel independent component analysis. J. Mach. Learn. Res. 3(Jul), 1–48 (2002)

    MathSciNet  MATH  Google Scholar 

  2. Borgwardt, K.M., Gretton, A., Rasch, M.J., Kriegel, H.P., Schölkopf, B., Smola, A.J.: Integrating structured biological data by kernel maximum mean discrepancy. Bioinformatics 22(14), e49–e57 (2006)

    Article  Google Scholar 

  3. Bosq, D.: Contribution à la théorie de l’estimation fonctionnelle. Institut de statistique de l’Université de Paris, Paris (1971)

    MATH  Google Scholar 

  4. Dedecker, J., Doukhan, P., Lang, G., José Rafael, L., Louhichi, S., Prieur, C.: The empirical process. In: Dedecker, J., Doukhan, P., Lang, G., José Rafael, L., Louhichi, S., Prieur, C. (eds.) Weak Dependence: With Examples and Applications, pp. 223–246. Springer, New York (2007). https://doi.org/10.1007/978-0-387-69952-3_10

    Chapter  Google Scholar 

  5. Evangelista, P.F., Embrechts, M.J., Szymanski, B.K.: Some properties of the gaussian kernel for one class learning. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds.) ICANN 2007. LNCS, vol. 4668, pp. 269–278. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74690-4_28

    Chapter  Google Scholar 

  6. Fortet, R., Mourier, E.: Convergence de la répartition empirique vers la répartition théorique. Annales scientifiques de l’École Normale Supérieure 70(3), 267–285 (1953)

    Article  MATH  Google Scholar 

  7. Gretton, A., Borgwardt, K.M., Rasch, M., Schölkopf, B., Smola, A.J.: A kernel method for the two-sample-problem. In: Advances in Neural Information Processing Systems, pp. 513–520 (2007)

    Google Scholar 

  8. Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.: Measuring statistical dependence with Hilbert-Schmidt norms. In: Jain, S., Simon, H.U., Tomita, E. (eds.) ALT 2005. LNCS (LNAI), vol. 3734, pp. 63–77. Springer, Heidelberg (2005). https://doi.org/10.1007/11564089_7

    Chapter  Google Scholar 

  9. Gretton, A., Herbrich, R., Smola, A.J.: The kernel mutual information. In: 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Proceedings, ICASSP 2003, vol. 4, pp. IV-880. IEEE (2003)

    Google Scholar 

  10. Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis, vol. 46. Wiley, New Jersy (2004)

    Google Scholar 

  11. Irrthum, A., Wehenkel, L., Geurts, P., et al.: Inferring regulatory networks from expression data using tree-based methods. PLoS ONE 5(9), e12776 (2010)

    Article  Google Scholar 

  12. Karlebach, G., Shamir, R.: Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol. 9(10), 770–780 (2008)

    Article  Google Scholar 

  13. Krus, D.J., Blackman, H.S.: Test reliability and homogeneity from the perspective of the ordinal test theory. Appl. Measur. Educ. 1(1), 79–88 (1988)

    Article  Google Scholar 

  14. Mall, R., Cerulo, L., Garofano, L., Frattini, V., Kunji, K., Bensmail, H., Sabedot, T.S., Noushmehr, H., Lasorella, A., Iavarone, A., Ceccarelli, M.: RGBM: regularized gradient boosting machines for identification of the transcriptional regulators of discrete glioma subtypes. Nucleic Acids Res. gky015 (2018). https://doi.org/10.1093/nar/gky015

  15. Mall, R., Jumutc, V., Langone, R., Suykens, J.A.: Representative subsets for big data learning using k-NN graphs. In: 2014 IEEE International Conference on Big Data (Big Data), pp. 37–42. IEEE (2014)

    Google Scholar 

  16. Mall, R., Suykens, J.A.: Very sparse LSSVM reductions for large-scale data. IEEE Trans. Neural Netw. Learn. Syst. 26(5), 1086–1097 (2015)

    Article  MathSciNet  Google Scholar 

  17. Marbach, D., Costello, J.C., Küffner, R., Vega, N.M., Prill, R.J., Camacho, D.M., Allison, K.R., Kellis, M., Collins, J.J., Stolovitzky, G., et al.: Wisdom of crowds for robust gene network inference. Nat. Methods 9(8), 796–804 (2012)

    Article  Google Scholar 

  18. Marbach, D., Prill, R.J., Schaffter, T., Mattiussi, C., Floreano, D., Stolovitzky, G.: Revealing strengths and weaknesses of methods for gene network inference. Proc. Nat. Acad. Sci. 107(14), 6286–6291 (2010)

    Article  Google Scholar 

  19. Marbach, D., Schaffter, T., Mattiussi, C., Floreano, D.: Generating realistic in silico gene networks for performance assessment of reverse engineering methods. J. Comput. Biol. 16(2), 229–239 (2009)

    Article  Google Scholar 

  20. Margolin, A.A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Dalla Favera, R., Califano, A.: Aracne: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinform. 7(1), S7 (2006)

    Article  Google Scholar 

  21. Nelsen, R.B.: An Introduction to Copulas. Springer, Heidelberg (2007). https://doi.org/10.1007/0-387-28678-0

    MATH  Google Scholar 

  22. Pál, D., Póczos, B., Szepesvári, C.: Estimation of rényi entropy and mutual information based on generalized nearest-neighbor graphs. In: Advances in Neural Information Processing Systems, pp. 1849–1857 (2010)

    Google Scholar 

  23. Petralia, F., Wang, P., Yang, J., Tu, Z.: Integrative random forest for gene regulatory network inference. Bioinformatics 31(12), i197–i205 (2015)

    Article  Google Scholar 

  24. Pinna, A., Soranzo, N., De La Fuente, A.: From knockouts to networks: establishing direct cause-effect relationships through graph analysis. PLoS ONE 5(10), e12912 (2010)

    Article  Google Scholar 

  25. Plaisier, C.L., O’Brien, S., Bernard, B., Reynolds, S., Simon, Z., Toledo, C.M., Ding, Y., Reiss, D.J., Paddison, P.J., Baliga, N.S.: Causal mechanistic regulatory network for glioblastoma deciphered using systems genetics network analysis. Cell Syst. 3(2), 172–186 (2016)

    Article  Google Scholar 

  26. Póczos, B., Ghahramani, Z., Schneider, J.: Copula-based kernel dependency measures. arXiv preprint arXiv:1206.4682 (2012)

  27. Prill, R.J., Marbach, D., Saez-Rodriguez, J., Sorger, P.K., Alexopoulos, L.G., Xue, X., Clarke, N.D., Altan-Bonnet, G., Stolovitzky, G.: Towards a rigorous assessment of systems biology models: the DREAM3 challenges. PLoS ONE 5(2), e9202 (2010)

    Article  Google Scholar 

  28. Rényi, A., et al.: On measures of entropy and information. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 547–561 (1961)

    Google Scholar 

  29. Sarmanov, O.: The maximum correlation coefficient (symmetrical case). Dokl. Akad. Nauk SSSR 120(4), 715–718 (1958)

    MathSciNet  MATH  Google Scholar 

  30. Schaffter, T., Marbach, D., Floreano, D.: Genenetweaver: in silico benchmark generation and performance profiling of network inference methods. Bioinformatics 27(16), 2263–2270 (2011)

    Article  Google Scholar 

  31. Schweizer, B., Wolff, E.F.: On nonparametric measures of dependence for random variables. Ann. Stat. 9(4), 879–885 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shannon, C.W., Weaver, W.: The Mathematical Theory of Communication. Press UoI, Urbana (1949)

    MATH  Google Scholar 

  33. Sławek, J., Arodź, T.: Ennet: inferring large gene regulatory networks from expression data using gradient boosting. BMC Syst. Biol. 7(1), 1 (2013)

    Article  Google Scholar 

  34. van Someren, E., Wessels, L., Backer, E., Reinders, M.: Genetic network modeling. Pharmacogenomics 3(4), 507–525 (2002)

    Article  MATH  Google Scholar 

  35. Steinwart, I.: On the influence of the kernel on the consistency of support vector machines. J. Mach. Learn. Res. 2(Nov), 67–93 (2001)

    MathSciNet  MATH  Google Scholar 

  36. Sun, X., Janzing, D., Schölkopf, B., Fukumizu, K.: A kernel-based causal learning algorithm. In: Proceedings of the 24th International Conference on Machine Learning, pp. 855–862. ACM (2007)

    Google Scholar 

  37. Székely, G.J., Rizzo, M.L., Bakirov, N.K., et al.: Measuring and testing dependence by correlation of distances. Ann. Stat. 35(6), 2769–2794 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Tsallis, C.: Possible generalization of Boltzmann-gibbs statistics. J. Stat. Phys. 52(1), 479–487 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  39. Weisstein, E.: Sklar’s theorem. Retrieved 4, 15 (2011)

    Google Scholar 

  40. Yip, K.Y., Alexander, R.P., Yan, K.K., Gerstein, M.: Improved reconstruction of in silico gene regulatory networks by integrating knockout and perturbation data. PLoS ONE 5(1), e8121 (2010)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Qatar Computing Research Institute, Hamad Bin Khalifa University, Doha, Qatar

    Hossam Al Meer, Raghvendra Mall, Ehsan Ullah & Halima Bensmail

  2. Department of Mathematics, Al Faisal University, Riyadh, Kingdom of Saudi Arabia

    Nasreddine Megrez

Authors
  1. Hossam Al Meer
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  2. Raghvendra Mall
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  3. Ehsan Ullah
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  4. Nasreddine Megrez
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  5. Halima Bensmail
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Corresponding authors

Correspondence to Raghvendra Mall or Halima Bensmail .

Editor information

Editors and Affiliations

  1. University of Granada, Granada, Spain

    Ignacio Rojas

  2. University of Granada, Granada, Spain

    Francisco Ortuño

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Al Meer, H., Mall, R., Ullah, E., Megrez, N., Bensmail, H. (2018). ISaaC: Identifying Structural Relations in Biological Data with Copula-Based Kernel Dependency Measures. In: Rojas, I., Ortuño, F. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2018. Lecture Notes in Computer Science(), vol 10813. Springer, Cham. https://doi.org/10.1007/978-3-319-78723-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-78723-7_6

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  • Print ISBN: 978-3-319-78722-0

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