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Theory and Methods

Sparse Multi-Dimensional Graphical Models: A Unified Bayesian Framework

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Pages 779-793 | Received 01 Jun 2015, Published online: 12 Apr 2017

References

  • Akdemir, D. , and Gupta, A. K. (2011), “Array Variate Random Variables With Multiway Kronecker Delta Covariance Matrix Structure,” Journal of Algebraic Statistics , 2, 98–113.
  • Allen, G. I. , Tibshirani, R. , et al. (2010), “Transposable Regularized Covariance Models With an Application to Missing Data Imputation,” The Annals of Applied Statistics , 4, 764–790.
  • Baladandayuthapani, V. , Talluri, R. , Ji, Y. , Coombes, K. R. , Lu, Y. , Hennessy, B. T. , Davies, M. A. , and Mallick, B. K. (2014), “Bayesian Sparse Graphical Models for Classification With Application to Protein Expression Data,” The Annals of Applied Statistics , 8, 1443–1468.
  • Banerjee, O. , El Ghaoui, L. , and 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.
  • Barbieri, M. M. , and Berger, J. O. (2004), “Optimal Predictive Model Selection,” The Annals of Statistics , 32, 870–897.
  • Bast, R. C. , Hennessy, B. , and Mills, G. B. (2009), “The Biology of Ovarian Cancer: New Opportunities for Translation,” Nature Reviews Cancer , 9, 415–428.
  • Breslow, N. E. , and Clayton, D. G. (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association , 88, 9–25.
  • Carvalho, C. M. , and Scott, J. G. (2009), “Objective Bayesian Model Selection in Gaussian Graphical Models,” Biometrika , 96, 497–512.
  • Carvalho, C. M. , and West, M. (2007), “Dynamic Matrix-Variate Graphical Models,” Bayesian Analysis , 2, 69–97.
  • Centers for Disease Control and Prevention (2012), “Vital Signs: Binge Drinking Prevalence, Frequency, and Intensity Among Adults-United States, 2010,” MMWR. Morbidity and Mortality Weekly Report , 61, 14.
  • Centers for Disease Control and Prevention (2013), Tobacco Control State Highlights 2012 . Atlanta: US Department of Health and Human Services, Centers for Disease Control and Prevention. National Center for Chronic Disease Prevention and Health Promotion, Office on Smoking and Health.
  • Chung, J. , Kuo, C. J. , Crabtree, G. R. , and Blenis, J. (1992), “Rapamycin-fkbp Specifically Blocks Growth-Dependent Activation of and Signaling by the 70 kd s6 Protein Kinases,” Cell , 69, 1227–1236.
  • Davies, M. , Hennessy, B. , and Mills, G. B. (2006), “Point Mutations of Protein Kinases and Individualised Cancer Therapy,” Expert Opinion on Pharmacotherapy , 7, 2243–2261.
  • Davies, S. , Holmes, A. , Lomo, L. , Steinkamp, M. P. , Kang, H. , Muller, C. Y. , and Wilson, B. S. (2014), “High Incidence of erbb3, erbb4, and met Expression in Ovarian Cancer,” International Journal of Gynecologic Pathology .
  • Davis, J. , and Goadrich, M. (2006), “The Relationship Between Precision-Recall and roc Curves,” in Proceedings of the 23rd international conference on Machine learning , ACM, pp. 233–240.
  • Dawid, A. P. (1981), “Some Matrix-Variate Distribution Theory: Notational Considerations and a Bayesian Application,” Biometrika , 68, 265–274.
  • Dawid, A. P. , and Lauritzen, S. L. (1993), “Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models,” The Annals of Statistics , pp. 1272–1317.
  • Dobra, A. , Hans, C. , Jones, B. , Nevins, J. R. , Yao, G. , and West, M. (2004), “Sparse Graphical Models for Exploring Gene Expression Data,” Journal of Multivariate Analysis , 90, 196–212.
  • 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.
  • Edwards, B. K. , Ward, E. , Kohler, B. A. , Eheman, C. , Zauber, A. G. , Anderson, R. N. , Jemal, A. , Schymura, M. J. , Lansdorp-Vogelaar, I. , Seeff, L. C. , et al. (2010), “Annual Report to the Nation on the Status of Cancer, 1975–2006, Featuring Colorectal Cancer Trends and Impact of Interventions (Risk Factors, Screening, and Treatment) to Reduce Future Rates,” Cancer , 116, 544–573.
  • Fan, J. , and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association , 96, 1348–1360.
  • Fitch, A. M. , Jones, M. B. , and Massam, H. (2014), “The Performance of Covariance Selection Methods That Consider Decomposable Models Only,” Bayesian Analysis , 9, 659–684.
  • Friedman, J. , Hastie, T. , and Tibshirani, R. (2008), “Sparse Inverse Covariance Estimation With the Graphical Lasso,” Biostatistics , 9, 432–441.
  • Friedman, N. , Linial, M. , Nachman, I. , and Pe’er, D. (2000), “Using Bayesian Networks to Analyze Expression Data,” Journal of Computational Biology , 7, 601–620.
  • Geiger, D. , and Heckerman, D. (2002), “Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions,” The Annals of Statistics , 30, 1412–1440.
  • Gupta, A. , and Nagar, D. (2000), “Matrix Variate Distributions,” Monographs and Surveys in Pure and Applied Mathematics, Boca Raton, FL: Chapman and Hall/CRC Press.
  • 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 , 388–400.
  • Kundu, S. , Baladandayuthapani, V. , and Mallick, B. K. (2013), “Bayes Regularized Graphical Model Estimation in High Dimensions,” arXiv:1308.3915 .
  • Lauritzen, S. L. (1996), Graphical Models (vol. 17), Oxford, UK: Oxford University Press.
  • Leng, C. , and Tang, C. Y. (2012), “Sparse Matrix Graphical Models,” Journal of the American Statistical Association , 107, 1187–1200.
  • Li, J. , Simpson, L. , Takahashi, M. , Miliaresis, C. , Myers, M. P. , Tonks, N. , and Parsons, R. (1998), “The pten/mmac1 Tumor Suppressor Induces Cell Death That is Rescued by the Akt/Protein Kinase b Oncogene,” Cancer Research , 58, 5667–5672.
  • Liang, F. , Song, Q. , and Qiu, P. (2015), “An Equivalent Measure of Partial Correlation Coefficients for High Dimensional Gaussian Graphical Models,” Journal of the American Statistical Association , 110, 1248–1265.
  • Liu, J. S. (1994), “The Collapsed Gibbs Sampler in Bayesian Computations With Applications to a Gene Regulation Problem,” Journal of the American Statistical Association , 89, 958–966.
  • Meinshausen, N. , and Bühlmann, P. (2006), “High-Dimensional Graphs and Variable Selection With the Lasso,” The Annals of Statistics , 1436–1462.
  • Mukhopadhyay, N. , Price, D. J. , Kyriakis, J. , Pelech, S. , Sanghera, J. , and Avruch, J. (1992), “An Array of Insulin-Activated, Proline-Directed Serine/Threonine Protein Kinases Phosphorylate the p70 s6 Kinase,” Journal of Biological Chemistry , 267, 3325–3335.
  • Romanelli, A. , Martin, K. A. , Toker, A. , and Blenis, J. (1999), “p70 s6 Kinase is Regulated by Protein Kinase cζ and Participates in a Phosphoinositide 3-Kinase-Regulated Signalling Complex,” Molecular and Cellular Biology , 19, 2921–2928.
  • Rosen, D. G. , Mercado-Uribe, I. , Yang, G. , Bast, R. C. , Amin, H. M. , Lai, R. , and Liu, J. (2006), “The Role of Constitutively Active Signal Transducer and Activator of Transcription 3 in Ovarian Tumorigenesis and Prognosis,” Cancer , 107(11), 2730–2740.
  • Roverato, A. (2000), “Cholesky Decomposition of a Hyper Inverse Wishart Matrix,” Biometrika , 87, 99–112.
  • Scott, J. G. , and Berger, J. O. (2010), “Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem,” The Annals of Statistics , 38, 2587–2619.
  • Scott, J. G. , and Carvalho, C. M. (2008), “Feature-Inclusion Stochastic Search for Gaussian Graphical Models,” Journal of Computational and Graphical Statistics , 17, 790–808.
  • Selvendiran, K. , Tong, L. , Vishwanath, S. , Bratasz, A. , Trigg, N. J. , Kutala, V. K. , Hideg, K. , and Kuppusamy, P. (2007), “Ef24 Induces g2/m Arrest and Apoptosis in Cisplatin-Resistant Human Ovarian Cancer Cells by Increasing Pten Expression,” Journal of Biological Chemistry , 282, 28609–28618.
  • Shojaie, A. , and Michailidis, G. (2010), “Penalized Principal Component Regression on Graphs for Analysis of Subnetworks,” in Advances in Neural Information Processing Systems , pp. 2155–2163.
  • Siegel, R. , Ma, J. , Zou, Z. , and Jemal, A. (2014), “Cancer Statistics, 2014,” CA: A Cancer Journal for Clinicians , 64, 9–29.
  • Spirtes, P. , Glymour, C. , and Scheines, R. (2000), Causation, Prediction, and Search (Vol. 81), Cambridge, MA: The MIT Press.
  • Stingo, F. , and Marchetti, G. M. (2015), “Efficient Local Updates for Undirected Graphical Models,” Statistics and Computing , 25, 159–171.
  • Stingo, F. C. , Chen, Y. A. , Vannucci, M. , Barrier, M. , and Mirkes, P. E. (2010), “A Bayesian Graphical Modeling Approach to Microrna Regulatory Network Inference,” The Annals of Applied Statistics , 4, 2024–2048.
  • Tanner, B. , Hasenclever, D. , Stern, K. , Schormann, W. , Bezler, M. , Hermes, M. , Brulport, M. , Bauer, A. , Schiffer, I. B. , Gebhard, S. , et al. (2006), “Erbb-3 Predicts Survival in Ovarian Cancer,” Journal of Clinical Oncology , 24, 4317–4323.
  • The Cancer Genome Atlas (2012), “Comprehensive Molecular Characterization of Human Colon and Rectal Cancer,” Nature , 487, 330–337.
  • Tibes, R. , Qiu, Y. , Lu, Y. , Hennessy, B. , Andreeff, M. , Mills, G. B. , and Kornblau, S. M. (2006), “Reverse Phase Protein Array: Validation of a Novel Proteomic Technology and Utility for Analysis of Primary Leukemia Specimens and Hematopoietic Stem Cells,” Molecular Cancer Therapeutics , 5, 2512–2521.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society , Series B, 267–288.
  • U. S. Cancer Statistics Working Group (2014), United States Cancer Statistics: 1999–2011 Incidence and Mortality Web-based Report , Atlanta: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention and National Cancer Atlanta: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention and National Cancer Institute. Available at www.cdc.gov/uscs .
  • van Dyk, D. A. , and Jiao, X. (2015), “Metropolis-Hastings Within Partially Collapsed Gibbs Samplers,” Journal of Computational and Graphical Statistics , 24, 301–327.
  • van Dyk, D. A. , and Park, T. (2008), “Partially Collapsed Gibbs Samplers: Theory and Methods,” Journal of the American Statistical Association , 103, 790–796.
  • Wang, H. , and West, M. (2009), “Bayesian Analysis of Matrix Normal Graphical Models,” Biometrika , 96, 821–834.
  • Weichsel, P. M. (1962), “The Kronecker Product of Graphs,” Proceedings of the American Mathematical Society , 13, 47–52.
  • Wermuth, N. (1980), “Linear Recursive Equations, Covariance Selection, and Path Analysis,” Journal of the American Statistical Association , 75, 963–972.
  • Whittaker, J. (2009), Graphical Models in Applied Multivariate Statistics (1st ed.), New York: Wiley.
  • Wilcoxon, F. (1945), “Individual Comparisons by Ranking Methods,” Biometrics Bulletin , 1, 80–83.
  • Yajima, M. , Telesca, D. , Ji, Y. , and Müller, P. (2015), “Detecting Differential Patterns of Interaction in Molecular Pathways,” Biostatistics , 16, 240–251.
  • Yin, J. , and Li, H. (2012), “Model Selection and Estimation in the Matrix Normal Graphical Model,” Journal of Multivariate Analysis , 107, 119–140.
  • Yuan, M. , and Lin, Y. (2007), “Model Selection and Estimation in the Gaussian Graphical Model,” Biometrika , 94, 19–35.
  • Zhou, S. (2014), “Gemini: Graph Estimation With Matrix Variate Normal Instances,” The Annals of Statistics , 42, 532–562.

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