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Articles

Long-tailed graphical model and frequentist inference of the model parameters for biological networks

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Pages 1591-1605 | Received 04 Oct 2019, Accepted 25 Feb 2020, Published online: 13 Mar 2020

References

  • Bolouri H, Engelhardt M. Computational modelling of gene regulatory networks – a primer. London: Imperial College Press; 2008.
  • Huang S. Gene expression profiling, genetic networks, cellular states: an integrating concept for tumorigenesis and drug discovery. J Mol Med. 2012;77:469–480.
  • Koller D, Friedman N. Probabilistic graphical models principles and techniques. Massachusetts (MA): MIT Press; 2009.
  • Shmulevich I, Dougherty ER, Seungchan K, et al. Sparse inverse covariance estimation with the graphical lasso. Bioinformatics. 2002;18:261–274.
  • Golightly A, Wilkonson DJ. Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics. 1998;58(61):788–871.
  • Wilkinson DJ. Stochastic modelling for systems biology. Boca Raton, Florida: Taylor and Francis; 2006.
  • Reinker S., Altman M, Timmer J. Parameter estimation in stochastic biochemical reactions. EEE Proc Sys Biol. 2006;153(4):168–178.
  • Defterli O, Purutçuoğlu V, Weber GW. Advance mathematical and statistical tools in the dynamic modelling and simulation of gene environment networks. In: Zilberman D, Pinto A, editors. Modeling, dynamics, optimization and bioeconomics I. New York (NY): Springer Proceedings in Mathematics and Statistics; 2006. p. 1–22.
  • Uğlur O, Pickl S, Weber W, et al. An algorithm approach to analyse genetic networks and biological energy production: an introduction and contribution where OR meets biology. Optimization. 2006;58(1):1–22.
  • Carlin BP, Louis TA. Bayes and empirical Bayes methods for data analysis. Boca Raton, Florida: Chapman and Hall/CRC; 2000.
  • Mohammadi R, Wit EC. BDgraph: an R package for Bayesian structure learning in graphical models. J Stat Softw. 2019;89(3):1–30.
  • Tibshrani R. Regression shrinkage and selection via the lasso. J R Stat Ser B. 1996;89(3):267–288.
  • Whittaker J. Graphical models in applied multivariate statistics. New York (NY): Wiley Publishing; 2009.
  • Dempster AP. Covariance selection. Biometrics. 2013;28(12):157–175.
  • Meinshausen N, Buhlmann P. High dimensional graphs and variable selection with the Lasso. Ann Stat. 2006;34(3):1436–1462.
  • Friedman JH, Hastie T, Tibshirani R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics. 2008;9(3):432–441.
  • Tibshrani R, Saunders M, Rosset S, et al. Sparsity and smoothness via the fused lasso. J R Stat Soc Ser B. 2005;67:91–108.
  • Zou H. The adaptive lasso and its oracle properties. J Am Stat Assoc. 2006;101(476):1418–1429.
  • Witten DM, Friedman JH, Simon N. New insights and faster computations for the graphical lasso. J Comput Graph Stat. 2011;20(4):892–900.
  • Ayyıldız E, Ağraz M, Purutçuoğlu V. MARS as the alternative approach of GGM in modelling of biochemical systems. J Appl Stat. 2016;44(16):2858–2876.
  • Ağraz M, Purutçuoğlu V. Extended lasso-type MARS model in the description of biological network. J Stat Comput Sim. 2019;89(1):1–14.
  • Ayyıldız E, Purutçuoğlu V, Weber GW. Loop-based conic multivariate adaptive regression splines is a novel method for advanced construction of complex biological networks. Eur J Oper Res. 2017;270(3):852–861.
  • Tiku ML. Estimating the mean and standard deviation from a censored normal sample. Biometrika. 1967;54(1):155–165.
  • Tiku ML, Tan W, Balakrishnan Y. Robust inference. New York (NY): Marcel Dekker Inc; 1986.
  • Tiku ML, Suresh RP. A new method of estimation for location and scale parameters. Biometrika. 1992;30(1):281–292.
  • Islam MQ. Estimation in multivariate normal distributions with stochastic variance function. J Comput Appl Math. 2014;255:698–714.
  • Mutan OC, Senoglu B. A Monte Carlo comparison of regression estimators when the error distribution is long-tailed symmetric. J Mod Appl Stat Methods. 2009;8(1):126–137.
  • Oral RE. Binary regression with stochastic covariates. CoSTM. 2006;35:1426–1447.
  • Dobra A, Lenkoski A. Copula Gaussian graphical models and their application to modeling functional disability data. Ann Appl Stat. 2011;5(2A):969–993.
  • Liu H, Lafferty J, Wasserman L. The nonparanormal: semiparametric estimation of high dimensional undirected graphs. J Mach Learn Res. 2009;10:2295–2328.
  • Morrison RE, Baptista R, Marzouk Y. Beyond normality: learning sparse probabilistic graphical models in the non-Gaussian setting Beyond normality. In: Guyon I, Luxburg UV, Bengio S, et al. editors. Advances in neural information processing systems 30. Curran Associates, Long Beach, CA, USA Inc; 2017; p. 2359–2369.
  • Bhadra A, Rao A, Baladandayuthapani V. Inferring network structure in non-normal and mixed discrete-continuous genomic data. Biometrics. 2018;74(1):185–195.
  • Ravikumar P, Wainwright MJ, Lafferty JD. High-dimensional ising model selection using ‘1- regularized logistic regression. Ann Statist. 2010;38(3):1287–1319.
  • Fellinghauer Buhlmann PB, Ryffel R, von Rhein M, et al. Stable graphical model estimation with random forests for discrete, continuous, and mixed variables. Comput Stat Data Anal. 2013;64:132–152.
  • Yuan M, Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika. 2007;94:19–35.
  • Bain LJ, Engelhardt M. Introduction to probability and mathematical statistics. 2nd ed. Pacific Grove, CA, USA: Duxbury Press; 1992.
  • Tiku ML. Modified maximum likelihood estimation. New York (NY): Encyclopedia of Statistical Science, Wiley; 1989.
  • Han L, Roeder K, Larry W. Stability approach to regularization selection (StARS) for high dimensional graphical models. In: Lafferty JD, Williams CKI, Shawe-Taylor J, et al. editors. Advances in neural information processing systems. Curran Associates Inc.; 2010, Vancover, BC, Canada p. 1432–1440.
  • Koch AL. The logarithm in biology. II. Mechanisms generating the lognormal distribution exactly. J Theor Biol. 1966;23:276–290.
  • Limpert E, Stahel WA, Abbt M. Log-normal distributions across the sciences: keys and clues. BioScience. 2001;51(5):341–351.
  • Sachs K, Perez O, Pe'Er O, et al. Causal protein-signaling networks derived from multiparameter single-cell data. Sciences. 2005;5721(308):523–529.
  • Bahcıvan B, Purutçuoğlu V, Ürün Y. Estimation of gynecological cancer networks via target proteins. J Multidiscip Eng Sci Technol. 2018;5(12):9296–9302.
  • Tothill R, Tinker A, George J, et al. Novel molecular subtypes of serious and endometrioid ovarian cancer linked to clinical outcome. Clin Cancer Res. 2008;14(16):5198–5208.
  • Abegaz F, Wit J. Sparse time series chain graphical models for reconstructing genetic networks. Biostatistics. 2013;14(3):586–599.
  • Mohammadi R, Wit EC. Optimization in computational systems biology. BMC Syst Biol. 2008;47(2):1–7.
  • Mohammadi R, Wit EC. Bayesian structure learning in sparse Gaussian graphical model. Bayesian Anal. 2015;10(1):109–135.

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