Joint Estimation of Multiple Dependent Gaussian Graphical Models with Applications to Mouse Genomics.
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ABSTRACT:
SUBMITTER: Xie Y
PROVIDER: S-EPMC5640885 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:In this article, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model converges to one. When there are multiple groups of data available, instead of estimating the networks independently for each group, joint estimation of the networks may utilize the shared information among groups and lead to improved estimation for each individual network. Our method is extended to jointly estimate GGMs in multiple groups of data with complex structures, including spatial data, temporal data, and data with both spatial and temporal structures. Markov random field (MRF) models are used to efficiently incorporate the complex data structures. We develop and implement an efficient algorithm for statistical inference that enables parallel computing. Simulation studies suggest that our approach achieves better accuracy in network estimation compared with methods not incorporating spatial and temporal dependencies when there are shared structures among the networks, and that it performs comparably well otherwise. Finally, we illustrate our method using the human brain gene expression microarray dataset, where the expression levels of genes are measured in different brain regions across multiple time periods.
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Project description:It is challenging to identify meaningful gene networks because biological interactions are often condition-specific and confounded with external factors. It is necessary to integrate multiple sources of genomic data to facilitate network inference. For example, one can jointly model expression datasets measured from multiple tissues with molecular marker data in so-called genetical genomic studies. In this paper, we propose a joint conditional Gaussian graphical model (JCGGM) that aims for modeling biological processes based on multiple sources of data. This approach is able to integrate multiple sources of information by adopting conditional models combined with joint sparsity regularization. We apply our approach to a real dataset measuring gene expression in four tissues (kidney, liver, heart, and fat) from recombinant inbred rats. Our approach reveals that the liver tissue has the highest level of tissue-specific gene regulations among genes involved in insulin responsive facilitative sugar transporter mediated glucose transport pathway, followed by heart and fat tissues, and this finding can only be attained from our JCGGM approach.
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Project description:The task of estimating a Gaussian graphical model in the high-dimensional setting is considered. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to a lasso penalty, is a well-studied approach for this task. A surprising connection between the graphical lasso and hierarchical clustering is introduced: the graphical lasso in effect performs a two-step procedure, in which (1) single linkage hierarchical clustering is performed on the variables in order to identify connected components, and then (2) a penalized log likelihood is maximized on the subset of variables within each connected component. Thus, the graphical lasso determines the connected components of the estimated network via single linkage clustering. The single linkage clustering is known to perform poorly in certain finite-sample settings. Therefore, the cluster graphical lasso, which involves clustering the features using an alternative to single linkage clustering, and then performing the graphical lasso on the subset of variables within each cluster, is proposed. Model selection consistency for this technique is established, and its improved performance relative to the graphical lasso is demonstrated in a simulation study, as well as in applications to a university webpage and a gene expression data sets.
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Project description:In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T, n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.
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Project description:Revealing biological networks is one key objective in systems biology. With microarrays, researchers now routinely measure expression profiles at the genome level under various conditions, and, such data may be utilized to statistically infer gene regulation networks. Gaussian graphical models (GGMs) have proven useful for this purpose by modeling the Markovian dependence among genes. However, a single GGM may not be adequate to describe the potentially differing networks across various conditions, and hence it is more natural to infer multiple GGMs from such data. In the present study, we propose a class of nonconvex penalty functions aiming at the estimation of multiple GGMs with a flexible joint sparsity constraint. We illustrate the property of our proposed nonconvex penalty functions by simulation study. We then apply the method to a gene expression data set from the GenCord Project, and show that our method can identify prominent pathways across different conditions.
| S-EPMC4743539 | biostudies-literature
Project description:BackgroundGraphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares.ResultsIn this article, we investigate a general framework for combining regularized regression methods with the estimation of Graphical Gaussian models. This framework includes various existing methods as well as two new approaches based on ridge regression and adaptive lasso, respectively. These methods are extensively compared both qualitatively and quantitatively within a simulation study and through an application to six diverse real data sets. In addition, all proposed algorithms are implemented in the R package "parcor", available from the R repository CRAN.ConclusionIn our simulation studies, the investigated non-sparse regression methods, i.e. Ridge Regression and Partial Least Squares, exhibit rather conservative behavior when combined with (local) false discovery rate multiple testing in order to decide whether or not an edge is present in the network. For networks with higher densities, the difference in performance of the methods decreases. For sparse networks, we confirm the Lasso's well known tendency towards selecting too many edges, whereas the two-stage adaptive Lasso is an interesting alternative that provides sparser solutions. In our simulations, both sparse and non-sparse methods are able to reconstruct networks with cluster structures. On six real data sets, we also clearly distinguish the results obtained using the non-sparse methods and those obtained using the sparse methods where specification of the regularization parameter automatically means model selection. In five out of six data sets, Partial Least Squares selects very dense networks. Furthermore, for data that violate the assumption of uncorrelated observations (due to replications), the Lasso and the adaptive Lasso yield very complex structures, indicating that they might not be suited under these conditions. The shrinkage approach is more stable than the regression based approaches when using subsampling.
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Project description:We consider the problem of estimating multiple related Gaussian graphical models from a high-dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso, which borrows strength across the classes in order to estimate multiple graphical models that share certain characteristics, such as the locations or weights of nonzero edges. Our approach is based upon maximizing a penalized log likelihood. We employ generalized fused lasso or group lasso penalties, and implement a fast ADMM algorithm to solve the corresponding convex optimization problems. The performance of the proposed method is illustrated through simulated and real data examples.
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Project description:Gene regulatory networks (GRNs) are often inferred based on Gaussian graphical models that could identify the conditional dependence among genes by estimating the corresponding precision matrix. Classical Gaussian graphical models are usually designed for single network estimation and ignore existing knowledge such as pathway information. Therefore, they can neither make use of the common information shared by multiple networks, nor can they utilize useful prior information to guide the estimation. In this paper, we propose a new weighted fused pathway graphical lasso (WFPGL) to jointly estimate multiple networks by incorporating prior knowledge derived from known pathways and gene interactions. Based on the assumption that two genes are less likely to be connected if they do not participate together in any pathways, a pathway-based constraint is considered in our model. Moreover, we introduce a weighted fused lasso penalty in our model to take into account prior gene interaction data and common information shared by multiple networks. Our model is optimized based on the alternating direction method of multipliers (ADMM). Experiments on synthetic data demonstrate that our method outperforms other five state-of-the-art graphical models. We then apply our model to two real datasets. Hub genes in our identified state-specific networks show some shared and specific patterns, which indicates the efficiency of our model in revealing the underlying mechanisms of complex diseases.
| S-EPMC6662592 | biostudies-literature
Project description:Despite major methodological developments, Bayesian inference in Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and conditional independence structures between variables by multiple testing, which bypasses the exploration of the model space. Specifically, we introduce closed-form Bayes factors under the Gaussian conjugate model to evaluate the null hypotheses of marginal and conditional independence between variables. Their computation for all pairs of variables is shown to be extremely efficient, thereby allowing us to address large problems with thousands of nodes as required by modern applications. Moreover, we derive exact tail probabilities from the null distributions of the Bayes factors. These allow the use of any multiplicity correction procedure to control error rates for incorrect edge inclusion. We demonstrate the proposed approach on various simulated examples as well as on a large gene expression data set from The Cancer Genome Atlas.
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Project description:The Cancer Genome Atlas (TCGA) provides a rich resource that can be used to understand how genes interact in cancer cells and has collected RNA-Seq gene expression data for many types of human cancer. However, mining the data to uncover the hidden gene-interaction patterns remains a challenge. Gaussian graphical model (GGM) is often used to learn genetic networks because it defines an undirected graphical structure, revealing the conditional dependences of genes. In this study, we focus on inferring gene interactions in 15 specific types of human cancer using RNA-Seq expression data and GGM with graphical lasso. We take advantage of the corresponding Kyoto Encyclopedia of Genes and Genomes pathway maps to define the subsets of related genes. RNA-Seq expression levels of the subsets of genes in solid cancerous tumor and normal tissues were extracted from TCGA. The gene expression data sets were cleaned and formatted, and the genetic network corresponding to each cancer type was then inferred using GGM with graphical lasso. The inferred networks reveal stable conditional dependences among the genes at the expression level and confirm the essential roles played by the genes that encode proteins involved in the two key signaling pathway phosphoinositide 3-kinase (PI3K)/AKT/mTOR and Ras/Raf/MEK/ERK in human carcinogenesis. These stable dependences elucidate the expression level interactions among the genes that are implicated in many different human cancers. The inferred genetic networks were examined to further identify and characterize a collection of gene interactions that are unique to cancer. The cross-cancer genetic interactions revealed from our study provide another set of knowledge for cancer biologists to propose strong hypotheses, so further biological investigations can be conducted effectively.
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