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Factorial graphical models for dynamic networks

Published online by Cambridge University Press:  12 February 2015

ERNST WIT  and
ANTONINO ABBRUZZO
ERNST WIT
Affiliation:
Johann Bernoulli Institute, University of Groningen, 9747 AG Groningen, the Netherlands (e-mail: [email protected])
ANTONINO ABBRUZZO
Affiliation:
Dipartimento Scienze Economiche, Aziendali e Statistiche, University of Palermo, 90128 Palermo, Italy
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Abstract

Dynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.

We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.

Keywords

constrained optimizationdynamic networksGaussian graphical modelspenalized likelihoodtime-course datagene networks
Type
Research Article
Information
Network Science , Volume 3 , Issue 1: Networks in Space and in Time: Methods and Applications , March 2015 , pp. 37 - 57
Copyright
Copyright © Cambridge University Press 2015 

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References

Banerjee, O., El Ghaoui, L., & d'Aspremont, A. (2008). Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data. The Journal of Machine Learning Research, 9, 485–516.Google Scholar
Bolstad, B. M., Irizarry, R. A., Åstrand, M., & Speed, T. P. (2003). A comparison of normalization methods for high density oligonucleotide array data based on variance and bias. Bioinformatics, 19 (2), 185–193.Google Scholar
Breiman, L. (1996). Heuristics of instability and stabilization in model selection. The Annals of Statistics, 24 (6), 2350–2383.Google Scholar
Dempster, A. P. (1972). Covariance selection. Biometrics, 28, 157–175.CrossRefGoogle Scholar
Drton, M., & Perlman, M. D. (2004). Model selection for gaussian concentration graphs. Biometrika, 91 (3), 591–602.Google Scholar
Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96 (456), 1348–1360.CrossRefGoogle Scholar
Foygel, R., & Drton, M. (2010). Extended bayesian information criteria for gaussian graphical models. Advances in Neural Information Processing Systems, 23, 604–612.Google Scholar
Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9 (3), 432–441.Google Scholar
Højsgaard, S., & Lauritzen, S. L. (2008). Graphical gaussian models with edge and vertex symmetries. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70 (5), 1005–1027.CrossRefGoogle Scholar
Jeong, H., Mason, S. P., Barabási, A. L., & Oltvai, Z. N. (2001). Lethality and centrality in protein networks. Nature, 411 (6833), 41–42. Nature Publishing Group.Google Scholar
Lam, C., & Fan, J. (2009). Sparsistency and rates of convergence in large covariance matrix estimation. Annals of Statistics, 37 (6B), 4254.Google Scholar
Lauritzen, S. L. (1996). Graphical models. Oxford: Clarendon Press.Google Scholar
Meinshausen, N. & Bühlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. The Annals of Statistics, 34 (3), 1436–1462.Google Scholar
Meinshausen, N. & Bühlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series b (Statistical Methodology), 72 (4), 417–473.Google Scholar
Maulana, R., Opdenakker, M. C., Stroet, K., & Bosker, R. (2013). Changes in teachers' involvement versus rejection and links with academic motivation during the first year of secondary education: A multilevel growth curve analysis, Journal of youth and adolescence, 42 (9), 1348–1371. Springer.Google Scholar
Peng, J., Wang, P., Zhou, N., & Zhu, J. (2009). Partial correlation estimation by joint sparse regression models. Journal of the American Statistical Association, 104 (486), 735–746.CrossRefGoogle ScholarPubMed
Rangel, C., Angus, J., Ghahramani, Z., Lioumi, M., Sotheran, E., Gaiba, A., . . . Falciani, F. (2004). Modeling t-cell activation using gene expression profiling and state-space models. Bioinformatics, 20 (9), 1361–1372.Google Scholar
Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J. (2008). Sparse permutation invariant covariance estimation. ElectronicJjournal of Statistics, 2, 494–515.Google Scholar
Snijders, T. A. B., Van de Bunt, G. G., & Steglich, C. E. G. (2010). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32 (1), 44–60.CrossRefGoogle Scholar
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58 (1), 267–288.CrossRefGoogle Scholar
Vujacic, I., Abbruzzo, A., & Wit, E. C. (2015). A computationally fast alternative to cross-validation in penalized Gaussian graphical models. Journal of Statistical Computation and Simulation. doi 10.1080/00949655.2014.992020, http://dx.doi.org/10.1080/00949655.2014.992020.Google Scholar
Wang, C., Sun, D., & Toh, K. C. (2010). Solving log-determinant optimization problems by a newton-cg primal proximal point algorithm. SIAM Journal on Optimization, 20 (6), 2994.Google Scholar
Yuan, M., & Lin, Y. (2007). Model selection and estimation in the gaussian graphical model. Biometrika, 94 (1), 19–35.Google Scholar