Abstract
Real-world entities comprising a complex system evolve as a function of time and respond to external perturbations. Dynamic Bayesian networks extend the fundamental ideas behind static Bayesian networks to model associations arising from the temporal dynamics between the entities of interest. This has to be contrasted with static Bayesian networks, which model the network structure from multiple independent realizations of the entities of a snapshot of the process. More importantly, incorporating the temporal signatures is useful in capturing possible feedback loops that are implicitly disregarded in the case of static Bayesian networks. Since feedback loops are ubiquitous in biological pathways, dynamic Bayesian network modeling is expected to result in better representations of such pathways.
In this chapter, we will introduce basic definitions and models for modeling associations from multivariate linear time series using dynamic Bayesian networks. Applications include modeling gene networks from expression data. Two broad classes of multivariate time series are considered: those whose statistical properties are invariant as a function of time and those whose properties do show change of time.
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References
Beal M, Falciani F, Ghahramani Z, Rangel C, Wild D (2005) A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics 21:349–356
Bera AK, Jarque CM (1981) Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence. Econ Lett 7(4):313–318
Chiquet J, Smith A, Grasseau G, Matias C, Ambroise C (2009) SIMoNe: statistical inference for modular networks. Bioinformatics 25(3):417–418
Csardi G, Nepusz T (2006) The igraph software package for complex network research. Int J Comp Syst:1695, pp 1–38
Dondelinger F, Lèbre S, Husmeier D (2013) Non-homogeneous dynamic Bayesian networks with Bayesian regularization for inferring gene regulatory networks with gradually time-varying structure. Machine Learning 90(2):191–230
Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2):407–499
Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4):987–1007
Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22
Goeman JJ (2012) penalized R package. R package version 0.9-41
Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4):711–732
Hamilton JD (1994) Time-series analysis. Princeton University Press, Princeton
Hastie T, Efron B (2012) lars: least angle regression, lasso and forward stagewise. R package version 1.1
Imoto S, Goto T, Miyano S (2002) Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. In: Proceedings of the 7th Pacific symposium on biocomputing, pp 175–186
Imoto S, Kim S, Goto T, Aburatani S, Tashiro K, Kuhara S, Miyano S (2003) Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network. J Bioinforma Comput Biol 2:231–252
James W, Stein C (1961) Estimation with quadratic loss. In: Neyman J (ed) Proceedings of the 4th Berkeley symposium on mathematical statistics and probability, pp 361–379
Jarque CM, Bera AK (1980) Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Econ Lett 6(3):255–259
Jarque CM, Bera AK (1987) A test for normality of observations and regression residuals. Int Stat Rev 55(2):163–172
Kim S, Imoto S, Miyano S (2003) Inferring gene networks from time series microarray data using dynamic Bayesian networks. Brief Bioinform 4(3):228
Kim S, Imoto S, Miyano S (2004) Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data. Biosystems 75(1–3):57–65
Lauritzen SL (1996) Graphical models. Oxford University Press, Oxford
Lèbre S (2008) G1DBN: a package performing dynamic Bayesian network inference. R package version 3.1
Lèbre S (2009) Inferring dynamic genetic networks with low order independencies. Stat Appl Genet Mol Biol 8(1):9
Lèbre S, Becq J, Devaux F, Lelandais G, Stumpf M (2010) Statistical inference of the time-varying structure of gene-regulation networks. BMC Syst Biol 4(130):1–16
Ledoit O, Wolf M (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J Empir Financ 10:603–621
Lütkepohl H (2005) New introduction to multiple time series analysis. Springer, New York
Meinshausen N, Bühlman P (2006) High dimensional graphs and variable selection with the LASSO. Ann Stat 34(3):1436–1462
Ong IM, Glasner JD, Page D (2002) Modelling regulatory pathways in E. Coli from time series expression profiles. Bioinformatics 18(Suppl 1):S241–S248
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 Bioinformatics 8(Suppl. 2):S3
Perrin BE, Ralaivola L, Mazurie A, Bottani S, Mallet J, d’Alché Buc F (2003) Gene networks inference using dynamic Bayesian networks. Bioinformatics 19(Suppl 2):S138–S148
Pfaff B (2008a) Analysis of integrated and cointegrated time series with R, 2nd edn. Springer, New York
Pfaff B (2008b) VAR, SVAR and SVEC models: implementation within R package vars. J Stat Softw 27(4):1–32
Rangel C, Angus J, Ghahramani Z, Lioumi M, Sotheran E, Gaiba A, Wild DL, Falciani F (2004) Modeling T-cell activation using gene expression profiling and state-space models. Bioinformatics 20(9):1361–1372
Shäfer J, Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genet Mol Biol 4:32
Smith SM, Fulton DC, Chia T, Thorneycroft D, Chapple A, Dunstan H, Hylton C, Zeeman SC, Smith AM (2004) Diurnal changes in the transcriptome encoding enzymes of starch metabolism provide evidence for both transcriptional and posttranscriptional regulation of starch metabolism in Arabidopsis leaves. Plant Physiol 136(1):2687–2699
Stein C (1956) Inadmissibility of the usual estimator for the mean of a multivariate distribution. In: Neyman J (ed) Proceedings of the 3rd Berkeley symposium on mathematical statistics and probability, pp 197–206
Sugimoto N, Iba H (2004) Inference of gene regulatory networks by means of dynamic differential Bayesian networks and nonparametric regression. Genome Inform 15(2):121–130
Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J R Stat Soc B 58(1): 267–288
Wu FX, Zhang WJ, Kusalik AJ (2004) Modeling gene expression from microarray expression data with state-space equations. In: Proceedings of the 9th Pacific Symposium on Biocomputing, pp 581–592
Zou M, Conzen SD (2005) A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics 21(1):71–79
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Nagarajan, R., Scutari, M., Lèbre, S. (2013). Bayesian Networks in the Presence of Temporal Information. In: Bayesian Networks in R. Use R!, vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6446-4_3
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DOI: https://doi.org/10.1007/978-1-4614-6446-4_3
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