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High‐dimensional covariance estimation for Gaussian directed acyclic graph models with given order

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Jerome Taylor, Kshitij Khare

Published Online: May 22 2019

DOI: 10.1002/wics.1468

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Abstract The covariance matrix is a fundamental quantity that helps us understand the nature of relationships among variables in a multivariate data set. Estimating the covariance matrix can be challenging in modern applications where the number of variables is often larger than the number of samples. In this paper, we review methods which tackle this challenge by inducing sparsity in the Cholesky parameter of the inverse covariance matrix. This article is categorized under: Algorithms and Computational Methods > Numerical Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data

The placement of zeros in the Cholesky factor T: (a) Banding; (b) Lasso penalty of Huang et al.; (c) adaptive banding

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References

Aragam,, B., Amini,, A., & Zhou,, Q. (2016). Learning directed acyclic graphs with penalized neighbourhood regression. arxiv:1511.08963.
Aragam,, B., & Zhou,, Q. (2015). Concave penalized estimation of sparse Gaussian bayesian networks. Journal of Machine Learning Research, 16, 2273–2328.
Ben‐David,, E., Li,, T., Massam,, H., & Rajaratnam,, B. (2011). High dimensional bayesian inference for Gaussian directed acyclic graph models. arXiv preprint arXiv:1109.4371.
Bickel,, P. J., & Levina,, E. (2008). Regularized estimation of large covariance matrices. The Annals of Statistics, 36(1), 199–227.
Cao,, X., Khare,, K., & Ghosh,, M. (2016). Posterior graph selection and estimation consistency for high‐dimensional bayesian dag models. arXiv preprint arXiv:1611.01205.
Consonni,, G., La Rocca,, L., & Peluso,, S. (2017). Objective Bayes covariate‐adjusted sparse graphical model selection. Scandinavian Journal of Statistics, 44(3), 741–764.
Geiger,, D., & Heckerman,, D. (2002). Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Annals of Statistics, 30(5), 1412–1440.
Huang,, J. Z., Liu,, N., Pourahmadi,, M., & Liu,, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood. Biometrika, 93(1), 85–98.
Khare,, K., Oh,, S.‐Y., Rahman,, S., & Rajaratnam,, B. (2019). A scalable sparse cholesky based approach for learning high‐dimensional covariance matrices in ordered data. Submitted for publication.
Khare,, K. & Rajaratnam,, B. (2014). Convergence of cyclic coordinatewise l1 minimization. arXiv preprint arXiv:1404.5100.
Letac,, G., & Massam,, H. (2007). Wishart distributions for decomposable graphs. The Annals of Statistics, 35(3), 1278–1323.
Levina,, E., Rothman,, A., & Zhu,, J. (2008). Sparse estimation of large covariance matrices via a nested lasso penalty. The Annals of Applied Statistics, 2(1), 245–263.
Pourahmadi,, M. (2011). Covariance estimation: The glm and regularization perspectives. Statistical Science, 26, 369–387.
Shojaie,, A., & Michailidis,, G. (2010). Penalized likelihood methods for estimation of sparse high‐dimensional directed acyclic graphs. Biometrika, 97(3), 519–538.
van de Geer,, S., & Buhlmann,, P. (2013). l0‐penalized maximum likelihood for sparse directed acyclic graphs. Annals of Statistics, 41, 536–567.
Wu,, W. B., & Pourahmadi,, M. (2003). Nonparametric estimation of large covariance matrices of longitudinal data. Biometrika, 90(4), 831–844.
Yu,, G., & Bien,, J. (2017). Learning local dependence in ordered data. Journal of Machine Learning Research, 18(42), 1–60.

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