Learning Bi-clustered Vector Autoregressive Models

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7524)


Vector Auto-regressive (VAR) models are useful for analyzing temporal dependencies among multivariate time series, known as Granger causality. There exist methods for learning sparse VAR models, leading directly to causal networks among the variables of interest. Another useful type of analysis comes from clustering methods, which summarize multiple time series by putting them into groups. We develop a methodology that integrates both types of analyses, motivated by the intuition that Granger causal relations in real-world time series may exhibit some clustering structure, in which case the estimation of both should be carried out together. Our methodology combines sparse learning and a nonparametric bi-clustered prior over the VAR model, conducting full Bayesian inference via blocked Gibbs sampling. Experiments on simulated and real data demonstrate improvements in both model estimation and clustering quality over standard alternatives, and in particular biologically more meaningful clusters in a T-cell activation gene expression time series dataset than those by other methods.


time-series analysis vector auto-regressive models bi-clustering Bayesian non-parametrics gene expression analysis 


  1. 1.
    Brock, G., Pihur, V., Datta, S., Datta, S.: clvalid: An R package for cluster validation. Journal of Statistical Software 25(4), 1–22 (2008)Google Scholar
  2. 2.
    Busygin, S., Prokopyev, O., Pardalos, P.: Biclustering in data mining. Computers & Operations Research 35(9), 2964–2987 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Cooke, E., Savage, R., Kirk, P., Darkins, R., Wild, D.: Bayesian hierarchical clustering for microarray time series data with replicates and outlier measurements. BMC Bioinformatics 12(1), 399 (2011)CrossRefGoogle Scholar
  4. 4.
    Datta, S., Datta, S.: Methods for evaluating clustering algorithms for gene expression data using a reference set of functional classes. BMC Bioinformatics 7(1), 397 (2006)CrossRefGoogle Scholar
  5. 5.
    Fujita, A., Sato, J., Garay-Malpartida, H., Yamaguchi, R., Miyano, S., Sogayar, M., Ferreira, C.: Modeling gene expression regulatory networks with the sparse vector autoregressive model. BMC Systems Biology 1(1), 39 (2007)CrossRefGoogle Scholar
  6. 6.
    Girvan, M., Newman, M.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences 99(12), 7821 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Granger, C.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 424–438 (1969)Google Scholar
  8. 8.
    Heller, K., Ghahramani, Z.: Bayesian hierarchical clustering. In: The 22nd International Conference on Machine Learning, pp. 297–304. ACM (2005)Google Scholar
  9. 9.
    Herman, I., Melançon, G., Marshall, M.: Graph visualization and navigation in information visualization: A survey. IEEE Transactions on Visualization and Computer Graphics 6(1), 24–43 (2000)CrossRefGoogle Scholar
  10. 10.
    Hubert, L., Arabie, P.: Comparing partitions. Journal of Classification 2(1), 193–218 (1985)CrossRefGoogle Scholar
  11. 11.
    Lozano, A., Abe, N., Liu, Y., Rosset, S.: Grouped graphical granger modeling for gene expression regulatory networks discovery. Bioinformatics 25(12), i110 (2009)CrossRefGoogle Scholar
  12. 12.
    Marlin, B.M., Schmidt, M., Murphy, K.P.: Group sparse priors for covariance estimation. In: Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009), Montreal, Canada (2009)Google Scholar
  13. 13.
    Meeds, E., Roweis, S.: Nonparametric Bayesian biclustering. Technical report, Department of Computer Science, University of Toronto (2007)Google Scholar
  14. 14.
    Mills, T.C.: The Econometric Modelling of Financial Time Series, 2nd edn. Cambridge University Press (1999)Google Scholar
  15. 15.
    Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems (2001)Google Scholar
  16. 16.
    Porteous, I., Bart, E., Welling, M.: Multi-hdp: A non-parametric bayesian model for tensor factorization. In: Proc. of the 23rd National Conf. on Artificial Intelligence, pp. 1487–1490 (2008)Google Scholar
  17. 17.
    Ramoni, M., Sebastiani, P., Kohane, I.: Cluster analysis of gene expression dynamics. Proceedings of the National Academy of Sciences 99(14), 9121 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Rangel, C., Angus, J., Ghahramani, Z., Lioumi, M., Sotheran, E., Gaiba, A., Wild, D., Falciani, F.: Modeling T-cell activation using gene expression profiling and state-space models. Bioinformatics 20(9), 1361–1372 (2004)CrossRefGoogle Scholar
  19. 19.
    Reimand, J., Arak, T., Vilo, J.: g: Profiler – a web server for functional interpretation of gene lists (2011 update). Nucleic Acids Research 39(suppl. 2), W307–W315 (2011)CrossRefGoogle Scholar
  20. 20.
    Schaeffer, S.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sethuraman, J.: A constructive definition of Dirichlet priors. Statistica Sinica 4, 639–650 (1994)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Shojaie, A., Basu, S., Michailidis, G.: Adaptive thresholding for reconstructing regulatory networks from time-course gene expression data. Statistics in Biosciences, 1–18 (2011)Google Scholar
  23. 23.
    Tsay, R.S.: Analysis of financial time series. Wiley-Interscience (2005)Google Scholar
  24. 24.
    Zou, H.: The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476), 1418–1429 (2006)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Computer ScienceCarnegie Mellon UniversityUSA

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