Fast hybrid Bayesian integrative learning of multiple gene regulatory networks for type 1 diabetes.

Motivated by the study of the molecular mechanism underlying type 1 diabetes with gene expression data collected from both patients and healthy controls at multiple time points, we propose a hybrid Bayesian method for jointly estimating multiple dependent Gaussian graphical models with data observed under distinct conditions, which avoids inversion of high-dimensional covariance matrices and thus can be executed very fast. We prove the consistency of the proposed method under mild conditions. The numerical results indicate the superiority of the proposed method over existing ones in both estimation accuracy and computational efficiency. Extension of the proposed method to joint estimation of multiple mixed graphical models is straightforward.

[1]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[3]  John D. Storey.  A direct approach to false discovery rates , 2002 .

[4]  Mark Goadrich,et al.  The relationship between Precision-Recall and ROC curves , 2006, ICML.

[5]  N. Meinshausen,et al.  High-dimensional graphs and variable selection with the Lasso , 2006, math/0608017.

[6]  F. Liang,et al.  Estimating the false discovery rate using the stochastic approximation algorithm , 2008 .

[7]  G. d’Annunzio,et al.  Variations of the Perforin Gene in Patients With Type 1 Diabetes , 2008, Diabetes.

[8]  John D. Storey,et al.  Mapping the Genetic Architecture of Gene Expression in Human Liver , 2008, PLoS biology.

[9]  Larry A. Wasserman,et al.  The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs , 2009, J. Mach. Learn. Res..

[10]  Jianqing Fan,et al.  Sure independence screening in generalized linear models with NP-dimensionality , 2009, The Annals of Statistics.

[11]  Larry A. Wasserman,et al.  Time varying undirected graphs , 2008, Machine Learning.

[12]  E. Levina,et al.  Joint estimation of multiple graphical models. , 2011, Biometrika.

[13]  D. Zaykin,et al.  Optimally weighted Z‐test is a powerful method for combining probabilities in meta‐analysis , 2011, Journal of evolutionary biology.

[14]  Junfeng Ma,et al.  Protein O-GlcNAcylation in diabetes and diabetic complications , 2013, Expert review of proteomics.

[15]  Å. Lernmark,et al.  Biomarker discovery study design for type 1 diabetes in The Environmental Determinants of Diabetes in the Young (TEDDY) study , 2014, Diabetes/metabolism research and reviews.

[16]  Patrick Danaher,et al.  The joint graphical lasso for inverse covariance estimation across multiple classes , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[17]  Christine B Peterson,et al.  Bayesian Inference of Multiple Gaussian Graphical Models , 2015, Journal of the American Statistical Association.

[18]  Takaya Saito,et al.  The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets , 2015, PloS one.

[19]  Trevor Hastie,et al.  Learning the Structure of Mixed Graphical Models , 2015, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[20]  Faming Liang,et al.  An Equivalent Measure of Partial Correlation Coefficients for High-Dimensional Gaussian Graphical Models , 2015 .

[21]  Hongyu Zhao,et al.  Gene Regulation Network Inference With Joint Sparse Gaussian Graphical Models , 2015, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[22]  Han Liu,et al.  Joint estimation of multiple graphical models from high dimensional time series , 2013, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[23]  Yufeng Liu,et al.  Joint estimation of multiple dependent Gaussian graphical models with applications to mouse genomics , 2016, Biometrika.

[24]  Yang I Li,et al.  An Expanded View of Complex Traits: From Polygenic to Omnigenic , 2017, Cell.

[25]  Tao Wang,et al.  On joint estimation of Gaussian graphical models for spatial and temporal data , 2015, Biometrics.

[26]  Faming Liang,et al.  Learning gene regulatory networks from next generation sequencing data , 2017, Biometrics.

[27]  Faming Liang,et al.  Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data , 2019, Neural Computation.