Statistics in Biosciences

, Volume 4, Issue 1, pp 66–83 | Cite as

Adaptive Thresholding for Reconstructing Regulatory Networks from Time-Course Gene Expression Data



Discovering regulatory interactions from time-course gene expression data constitutes a canonical problem in functional genomics and systems biology. The framework of graphical Granger causality allows one to estimate such causal relationships from these data. In this study, we propose an adaptively thresholding estimates of Granger causal effects obtained from the lasso penalization method. We establish the asymptotic properties of the proposed technique, and discuss the advantages it offers over competing methods, such as the truncating lasso. Its performance and that of its competitors is assessed on a number of simulated settings and it is applied on a data set that captures the activation of T-cells.


Regulatory networks Time-course gene expression data Graphical Granger causality Thresholding Lasso 


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  1. 1.
    Arnold A, Liu Y, Abe N (2007) Temporal causal modeling with graphical granger methods. In: Proceedings of the 13th ACM SIGKDD, pp 66–75 Google Scholar
  2. 2.
    Basu S, Shojaie A, Michailidis G (2011) Incorporating group structure in estimation of graphical Granger causality. Tech rep, Department of Statistics, University of Michigan Google Scholar
  3. 3.
    Bickel P, Ritov Y, Tsybakov A (2009) Simultaneous analysis of lasso and Dantzig selector. Ann Stat 37(4):1705–1732 MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Fujita A, Sato J, Garay-Malpartida H, Yamaguchi R, Miyano S, Sogayar M, Ferreira C (2007) Modeling gene expression regulatory networks with the sparse vector autoregressive model. BMC Syst Biol 1(1):39 CrossRefGoogle Scholar
  5. 5.
    Granger C (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 424–438 Google Scholar
  6. 6.
    Lozano A, Abe N, Liu Y, Rosset S (2009) Grouped graphical Granger modeling for gene expression regulatory networks discovery. Bioinformatics 25(12):i110 CrossRefGoogle Scholar
  7. 7.
    Lütkepohl H (2005) New introduction to multiple time series analysis. Springer, Berlin MATHGoogle Scholar
  8. 8.
    Meinshausen N, Yu B (2009) Lasso-type recovery of sparse representations for high-dimensional data. Ann Stat 37(1):246–270 MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Mukhopadhyay N, Chatterjee S (2007) Causality and pathway search in microarray time series experiment. Bioinformatics 23(4):442 CrossRefGoogle Scholar
  10. 10.
    Murphy K (2002) Dynamic Bayesian networks: representation, inference and learning. PhD thesis, University of California Google Scholar
  11. 11.
    Ong I, Glasner J, Page D et al. (2002) Modelling regulatory pathways in E. coli from time series expression profiles. Bioinformatics 18(Suppl 1):S241–S248 CrossRefGoogle Scholar
  12. 12.
    Opgen-Rhein R, Strimmer K (2007) Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process. BMC Bioinform 8(Suppl 2):S3 CrossRefGoogle Scholar
  13. 13.
    Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, Cambridge MATHGoogle Scholar
  14. 14.
    Perrin B, Ralaivola L, Mazurie A, Bottani S, Mallet J, d’Alche Buc F (2003) Gene networks inference using dynamic Bayesian networks. Bioinformatics 19(Suppl 2):138–148 CrossRefGoogle Scholar
  15. 15.
    Rangel C, Angus J, Ghahramani Z, Lioumi M, Sotheran E, Gaiba A, Wild D, Falciani F (2004) Modeling t-cell activation using gene expression profiling and state-space models. Bioinformatics 20(9):1361 CrossRefGoogle Scholar
  16. 16.
    Raskutti G, Wainwright MJ, Yu B (2010) Restricted eigenvalue properties for correlated Gaussian designs. J Mach Learn Res 11:2241–2259 MathSciNetGoogle Scholar
  17. 17.
    Shojaie A, Michailidis G (2010) Discovering graphical Granger causality using the truncating lasso penalty. Bioinformatics 26(18):i517–i523 CrossRefGoogle Scholar
  18. 18.
    Shojaie A, Michailidis G (2010) Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97(3):519–538 MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    van de Geer SA, Bühlmann P (2009) On the conditions used to prove oracle results for the lasso. Electron J Stat 3:1360–1392 MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wasserman L, Roeder K (2009) High dimensional variable selection. Ann Stat 37(5A):2178 MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Yamaguchi R, Yoshida R, Imoto S, Higuchi T, Miyano S (2007) Finding module-based gene networks with state-space models-Mining high-dimensional and short time-course gene expression data. IEEE Signal Process Mag 24(1):37–46 CrossRefGoogle Scholar
  22. 22.
    Zhou S (2010) Thresholded lasso for high dimensional variable selection and statistical estimation. Preprint arXiv:1002.1583

Copyright information

© International Chinese Statistical Association 2011

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity of WashingtonSeattleUSA
  2. 2.Department of StatisticsUniversity of MichiganAnn ArborUSA

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