An Expectation Conditional Maximization Approach for Gaussian Graphical Models

References

• Akaike, H. (1998), “Information Theory and an Extension of the Maximum Likelihood Principle,” in Selected Papers of Hirotugu Akaike, New York: Springer, pp. 199–213.
   Google Scholar
• Bu, Y., and Lederer, J. (2017), “Integrating Additional Knowledge Into Estimation of Graphical Models,” arXiv no. 1704.02739.
   Google Scholar
• Butts, C. T. (2008), “network: A Package for Managing Relational Data in R,” Journal of Statistical Software, 24, 1–36. DOI:10.18637/jss.v024.i02.
   PubMedGoogle Scholar
• Byass, P., Chandramohan, D., Clark, S. J., D’Ambruoso, L., Fottrell, E., Graham, W. J., Herbst, A. J., Hodgson, A., Hounton, S., Kahn, K., and Krishnan, A. (2012), “Strengthening Standardised Interpretation of Verbal Autopsy Data: The New InterVA-4 Tool,” Global Health Action, 5, 19281. DOI:10.3402/gha.v5i0.19281.
   PubMed Web of Science ®Google Scholar
• Cai, T. T., Zhang, C. H., and Zhou, H. H. (2010), “Optimal Rates of Convergence for Covariance Matrix Estimation,” Annals of Statistics, 38, 2118–2144. DOI:10.1214/09-AOS752.
   Web of Science ®Google Scholar
• Delyon, B., Lavielle, M., and Moulines, E. (1999), “Convergence of a Stochastic Approximation Version of the EM Algorithm,” Annals of Statistics, 27, 94–128. DOI:10.1214/aos/1018031103.
   Web of Science ®Google Scholar
• Deshpande, S. K., Rockova, V., and George, E. I. (2017), “Simultaneous Variable and Covariance Selection With the Multivariate Spike-and-Slab Lasso,” arXiv no. 1708.08911. DOI:10.1080/10618600.2019.1593179.
   Google Scholar
• Dobra, A., Lenkoski, A., and Rodriguez, A. (2011), “Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data,” Journal of the American Statistical Association, 106, 1418–1433. DOI:10.1198/jasa.2011.tm10465.
   PubMed Web of Science ®Google Scholar
• Eddelbuettel, D., and François, R. (2011), “Rcpp: Seamless R and C++ Integration,” Journal of Statistical Software, 40, 1–18. DOI:10.18637/jss.v040.i08.
   Web of Science ®Google Scholar
• Fan, J., Feng, Y., and Wu, Y. (2009), “Network Exploration via the Adaptive Lasso and Scad Penalties,” The Annals of Applied Statistics, 3, 521. DOI:10.1214/08-AOAS215SUPP.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation With the Graphical Lasso,” Biostatistics, 9, 432–441. DOI:10.1093/biostatistics/kxm045.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Applications of the Lasso and Grouped Lasso to the Estimation of Sparse Graphical Models,” Technical Report, pp. 1–22.
   Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2018), “glasso: Graphical Lasso: Estimation of Gaussian Graphical Models,” R Package Version 1.10.
   Google Scholar
• George, E. I., and McCulloch, R. E. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881–889. DOI:10.1080/01621459.1993.10476353.
   Web of Science ®Google Scholar
• Hoff, P. D. (2007), “Extending the Rank Likelihood for Semiparametric Copula Estimation,” The Annals of Applied Statistics, 1, 265–283.
   Web of Science ®Google Scholar
• Horton, R. (2007), “Counting for Health,” Lancet, 370, 1526. DOI:10.1016/S0140-6736(07)61418-4.
   PubMed Web of Science ®Google Scholar
• Ishwaran, H., and Rao, J. S. (2003), “Detecting Differentially Expressed Genes in Microarrays Using Bayesian Model Selection,” Journal of the American Statistical Association, 98, 438–455. DOI:10.1198/016214503000224.
   Web of Science ®Google Scholar
• Jones, B., Carvalho, C., Dobra, A., Hans, C., Carter, C., and West, M. (2005), “Experiments in Stochastic Computation for High-Dimensional Graphical Models,” Statistical Science, 20, 388–400. DOI:10.1214/088342305000000304.
   Web of Science ®Google Scholar
• Lauritzen, S. L. (1996), Graphical Models (Vol. 17), New York: Clarendon Press.
   Google Scholar
• Lenkoski, A., and Dobra, A. (2011), “Computational Aspects Related to Inference in Gaussian Graphical Models With the G-Wishart Prior,” Journal of Computational and Graphical Statistics, 20, 140–157. DOI:10.1198/jcgs.2010.08181.
   Web of Science ®Google Scholar
• Levine, R. A., and Casella, G. (2001), “Implementations of the Monte Carlo EM Algorithm,” Journal of Computational and Graphical Statistics, 10, 422–439. DOI:10.1198/106186001317115045.
   Web of Science ®Google Scholar
• Li, Z. R., McCormick, T., and Clark, S. (2019), “openVA: Automated Method for Verbal Autopsy,” R Package Version 1.0.8.
   Google Scholar
• Liu, H., Lafferty, J., and Wasserman, L. (2009), “The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs,” Journal of Machine Learning Research, 10, 2295–2328.
   Web of Science ®Google Scholar
• Liu, H., Roeder, K., and Wasserman, L. (2010), “Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models,” in Advances in Neural Information Processing Systems, pp. 1432–1440.
   PubMedGoogle Scholar
• Lukemire, J., Kundu, S., Pagnoni, G., and Guo, Y. (2017), “Bayesian Joint Modeling of Multiple Brain Functional Networks,” arXiv no. 1708.02123.
   Google Scholar
• Lysen, S. (2009), “Permuted Inclusion Criterion: A Variable Selection Technique,” Publicly Accessible Penn Dissertations, p. 28.
   Google Scholar
• Mazumder, R., and Hastie, T. (2012), “The Graphical Lasso: New Insights and Alternatives,” Electronic Journal of Statistics, 6, 2125. DOI:10.1214/12-EJS740.
   PubMed Web of Science ®Google Scholar
• McCormick, T. H., Li, Z. R., Calvert, C., Crampin, A. C., Kahn, K., and Clark, S. J. (2016), “Probabilistic Cause-of-Death Assignment Using Verbal Autopsies,” Journal of the American Statistical Association, 111, 1036–1049. DOI:10.1080/01621459.2016.1152191.
   PubMed Web of Science ®Google Scholar
• Meinshausen, N., and Bühlmann, P. (2006), “High-Dimensional Graphs and Variable Selection With the Lasso,” The Annals of Statistics, 34, 1436–1462. DOI:10.1214/009053606000000281.
   Web of Science ®Google Scholar
• Meng, X.-L., and Rubin, D. B. (1993), “Maximum Likelihood Estimation via the ECM Algorithm: A General Framework,” Biometrika, 80, 267–278. DOI:10.1093/biomet/80.2.267.
   Web of Science ®Google Scholar
• Mohammadi, A., Abegaz, F., van den Heuvel, E., and Wit, E. C. (2017), “Bayesian Modelling of Dupuytren Disease by Using Gaussian Copula Graphical Models,” Journal of the Royal Statistical Society, Series C, 66, 629–645. DOI:10.1111/rssc.12171.
   Web of Science ®Google Scholar
• Mohammadi, A., and Wit, E. C. (2015), “BDgraph: An R Package for Bayesian Structure Learning in Graphical Models,” arXiv no. 1501.05108.
   Google Scholar
• Murray, C. J., Lopez, A. D., Black, R., Ahuja, R., Ali, S. M., Baqui, A., Dandona, L., Dantzer, E., Das, V., Dhingra, U., and Dutta, A. (2011), “Population Health Metrics Research Consortium Gold Standard Verbal Autopsy Validation Study: Design, Implementation, and Development of Analysis Datasets,” Population Health Metrics, 9, 27. DOI:10.1186/1478-7954-9-27.
   PubMed Web of Science ®Google Scholar
• Nelsen, R. B. (1999), An Introduction to Copulas, Lecture Notes in Statistics (Vol. 139), New York: Springer-Verlag.
   Google Scholar
• Nielsen, S. F. (2000), “The Stochastic EM Algorithm: Estimation and Asymptotic Results,” Bernoulli, 6, 457–489. DOI:10.2307/3318671.
   Web of Science ®Google Scholar
• Peterson, C. B., Stingo, F. C., and Vannucci, M. (2015), “Joint Bayesian Variable and Graph Selection for Regression Models With Network-Structured Predictors,” Statistics in Medicine, 35, 1017–1031. DOI:10.1002/sim.6792.
   PubMed Web of Science ®Google Scholar
• Peterson, C., Vannucci, M., Karakas, C., Choi, W., Ma, L., and Meletić-Savatić, M. (2013), “Inferring Metabolic Networks Using the Bayesian Adaptive Graphical Lasso With Informative Priors,” Statistics and Its Interface, 6, 547. DOI:10.4310/SII.2013.v6.n4.a12.
   PubMed Web of Science ®Google Scholar
• R Core Team (2018), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Rocková, V. (2018), “Particle EM for Variable Selection,” Journal of the American Statistical Association, 113, 1684–1697.
   Web of Science ®Google Scholar
• Ročková, V., and George, E. I. (2014), “EMVS: The EM Approach to Bayesian Variable Selection,” Journal of the American Statistical Association, 109, 828–846. DOI:10.1080/01621459.2013.869223.
   Web of Science ®Google Scholar
• Rothman, A. J., Bickel, P. J., Levina, E., and Zhu, J. (2008), “Sparse Permutation Invariant Covariance Estimation,” Electronic Journal of Statistics, 2, 494–515. DOI:10.1214/08-EJS176.
   Web of Science ®Google Scholar
• Roverato, A. (2002), “Hyper Inverse Wishart Distribution for Non-decomposable Graphs and Its Application to Bayesian Inference for Gaussian Graphical Models,” Scandinavian Journal of Statistics, 29, 391–411. DOI:10.1111/1467-9469.00297.
   Web of Science ®Google Scholar
• Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461–464. DOI:10.1214/aos/1176344136.
   Web of Science ®Google Scholar
• Serina, P., Riley, I., Stewart, A., Flaxman, A. D., Lozano, R., Mooney, M. D., Luning, R., Hernandez, B., Black, R., Ahuja, R., and Alam, N. (2015), “A Shortened Verbal Autopsy Instrument for Use in Routine Mortality Surveillance Systems,” BMC Medicine, 13, 1. DOI:10.1186/s12916-015-0528-8.
   PubMed Web of Science ®Google Scholar
• Sing, T., Sander, O., Beerenwinkel, N., and Lengauer, T. (2005), “ROCR: Visualizing Classifier Performance in R,” Bioinformatics, 21, 7881. DOI:10.1093/bioinformatics/bti623.
   Web of Science ®Google Scholar
• Wakefield, J., De Vocht, F., and Hung, R. J. (2010), “Bayesian Mixture Modeling of Gene-Environment and Gene-Gene Interactions,” Genetic Epidemiology, 34, 16–25. DOI:10.1002/gepi.20429.
   PubMed Web of Science ®Google Scholar
• Wang, H. (2012), “Bayesian Graphical Lasso Models and Efficient Posterior Computation,” Bayesian Analysis, 7, 867–886. DOI:10.1214/12-BA729.
   Web of Science ®Google Scholar
• Wang, H. (2015), “Scaling It Up: Stochastic Search Structure Learning in Graphical Models,” Bayesian Analysis, 10, 351–377.
   Web of Science ®Google Scholar
• Wang, H., and Li, S. Z. (2012), “Efficient Gaussian Graphical Model Determination Under G-Wishart Prior Distributions,” Electronic Journal of Statistics, 6, 168–198. DOI:10.1214/12-EJS669.
   Web of Science ®Google Scholar
• Wei, G. C., and Tanner, M. A. (1990), “A Monte Carlo Implementation of the EM Algorithm and the Poor Man’s Data Augmentation Algorithms,” Journal of the American statistical Association, 85, 699–704. DOI:10.1080/01621459.1990.10474930.
   Web of Science ®Google Scholar
• Wei, T., and Simko, V. (2017), “R Package ‘corrplot’: Visualization of a Correlation Matrix,” Version 0.84.
   Google Scholar
• Wickham, H. (2007), “Reshaping Data With the Reshape Package,” Journal of Statistical Software, 21, 1–20. DOI:10.18637/jss.v021.i12.
   Web of Science ®Google Scholar
• Wickham, H. (2016), ggplot2: Elegant Graphics for Data Analysis, New York: Springer-Verlag.
   Google Scholar
• Wilhelm, S., and Manjunath, B. G. (2015), “tmvtnorm: Truncated Multivariate Normal and Student t Distribution,” R Package Version 1.4–10.
   Google Scholar
• Witten, D. M., Friedman, J. H., and Simon, N. (2011), “New Insights and Faster Computations for the Graphical Lasso,” Journal of Computational and Graphical Statistics, 20, 892–900. DOI:10.1198/jcgs.2011.11051a.
   Web of Science ®Google Scholar
• Xue, L. (2012), “Regularized Learning of High-Dimensional Sparse Graphical Models,” PhD Thesis, University of Minnesota.
   Google Scholar
• Xue, L., and Zou, H. (2012), “Regularized Rank-Based Estimation of High-Dimensional Nonparanormal Graphical Models,” The Annals of Statistics, 40, 2541–2571. DOI:10.1214/12-AOS1041.
   Web of Science ®Google Scholar
• Yin, J., and Li, H. (2011), “A Sparse Conditional Gaussian Graphical Model for Analysis of Genetical Genomics Data,” The Annals of Applied Statistics, 5, 2630. DOI:10.1214/11-AOAS494.
   PubMed Web of Science ®Google Scholar
• Yuan, M., and Lin, Y. (2007), “Model Selection and Estimation in the Gaussian Graphical Model,” Biometrika, 94, 19–35. DOI:10.1093/biomet/asm018.
   Web of Science ®Google Scholar
• Zhao, T., Liu, H., Roeder, K., Lafferty, J., and Wasserman, L. (2012), “The Huge Package for High-Dimensional Undirected Graph Estimation in R,” Journal of Machine Learning Research, 13, 1059–1062.
   Google Scholar