nips nips2012 nips2012-346 nips2012-346-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Marcelo Fiori, Pablo Musé, Guillermo Sapiro
Abstract: Graphical models are a very useful tool to describe and understand natural phenomena, from gene expression to climate change and social interactions. The topological structure of these graphs/networks is a fundamental part of the analysis, and in many cases the main goal of the study. However, little work has been done on incorporating prior topological knowledge onto the estimation of the underlying graphical models from sample data. In this work we propose extensions to the basic joint regression model for network estimation, which explicitly incorporate graph-topological constraints into the corresponding optimization approach. The first proposed extension includes an eigenvector centrality constraint, thereby promoting this important prior topological property. The second developed extension promotes the formation of certain motifs, triangle-shaped ones in particular, which are known to exist for example in genetic regulatory networks. The presentation of the underlying formulations, which serve as examples of the introduction of topological constraints in network estimation, is complemented with examples in diverse datasets demonstrating the importance of incorporating such critical prior knowledge. 1
Banerjee, O., El Ghaoui, L., and D’Aspremont, A. Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data. Journal of Machine Learning Research, 9:485–516, 2008. Barab´ si, A. and Albert, R. Emergence of scaling in random networks. Science, 286(5439):509–512, a 1999. Dempster, A. Covariance selection. Biometrics, 28(1):157–175, 1972. Friedman, J., Hastie, T., and Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3):432–41, July 2008. Friedman, J., Hastie, T., and Tibshirani, R. Applications of the lasso and grouped lasso to the estimation of sparse graphical models. Technical report, 2010. Kalisch, M. and B¨ hlmann, P. Estimating high-dimensional directed acyclic graphs with the PCu Algorithm. Journal of Machine Learning Research, 8:613–636, 2007. Lauritzen, S. Graphical Models. Clarendon Press, Oxford, 1996. Liu, Q. and Ihler, A. Learning scale free networks by reweighted 1 regularization. AI & Statistics, 15:40–48, April 2011. Meinshausen, N. and B¨ hlmann, P. High-dimensional graphs and variable selection with the Lasso. u The Annals of Statistics, 34(3):1436–1462, June 2006. Newman, M. Networks: An Introduction. Oxford University Press, Inc., New York, NY, USA, 2010. Peng, J., Wang, P., Zhou, N., and Zhu, J. Partial correlation estimation by joint sparse regression models. Journal of the American Statistical Association, 104(486):735–746, June 2009. Shen-Orr, S., Milo, R., Mangan, S., and Alon, U. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31(1):64–8, May 2002. Tibshirani, R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B, 58:267–288, 1996. Wolf, L. and Shashua, A. Feature selection for unsupervised and supervised inference: The emergence of sparsity in a weight-based approach. Journal of Machine Learning Research, 6:1855– 1887, 2005. Wright, S., Nowak, R., and Figueiredo, M. Sparse reconstruction by separable approximation. IEEE Transactions on Signal Processing, 57(7):2479–2493, 2009. Yuan, M. and Lin, Y. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B, 68(1):49–67, 2006. Yuan, M. and Lin, Y. Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1):19–35, February 2007. Zeitouni, O. Personal communication, 2012. 9