Application of graphical lasso in estimating network structure in gene set.
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ABSTRACT:
SUBMITTER: Huang YJ
PROVIDER: S-EPMC7791228 | biostudies-literature | 2020 Dec
REPOSITORIES: biostudies-literature
Publications
Application of graphical lasso in estimating network structure in gene set.
Huang Yu-Jyun YJ Lu Tzu-Pin TP Hsiao Chuhsing Kate CK
Annals of translational medicine 20201201 23
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Project description:BackgroundIdentifying gene interactions is a topic of great importance in genomics, and approaches based on network models provide a powerful tool for studying these. Assuming a Gaussian graphical model, a gene association network may be estimated from multiomic data based on the non-zero entries of the inverse covariance matrix. Inferring such biological networks is challenging because of the high dimensionality of the problem, making traditional estimators unsuitable. The graphical lasso is constructed for the estimation of sparse inverse covariance matrices in such situations, using [Formula: see text]-penalization on the matrix entries. The weighted graphical lasso is an extension in which prior biological information from other sources is integrated into the model. There are however issues with this approach, as it naïvely forces the prior information into the network estimation, even if it is misleading or does not agree with the data at hand. Further, if an associated network based on other data is used as the prior, the method often fails to utilize the information effectively.ResultsWe propose a novel graphical lasso approach, the tailored graphical lasso, that aims to handle prior information of unknown accuracy more effectively. We provide an R package implementing the method, tailoredGlasso. Applying the method to both simulated and real multiomic data sets, we find that it outperforms the unweighted and weighted graphical lasso in terms of all performance measures we consider. In fact, the graphical lasso and weighted graphical lasso can be considered special cases of the tailored graphical lasso, and a parameter determined by the data measures the usefulness of the prior information. We also find that among a larger set of methods, the tailored graphical is the most suitable for network inference from high-dimensional data with prior information of unknown accuracy. With our method, mRNA data are demonstrated to provide highly useful prior information for protein-protein interaction networks.ConclusionsThe method we introduce utilizes useful prior information more effectively without involving any risk of loss of accuracy should the prior information be misleading.
| S-EPMC8518261 | biostudies-literature
Project description:BackgroundConventional differential gene expression analysis by methods such as student's t-test, SAM, and Empirical Bayes often searches for statistically significant genes without considering the interactions among them. Network-based approaches provide a natural way to study these interactions and to investigate the rewiring interactions in disease versus control groups. In this paper, we apply weighted graphical LASSO (wgLASSO) algorithm to integrate a data-driven network model with prior biological knowledge (i.e., protein-protein interactions) for biological network inference. We propose a novel differentially weighted graphical LASSO (dwgLASSO) algorithm that builds group-specific networks and perform network-based differential gene expression analysis to select biomarker candidates by considering their topological differences between the groups.ResultsThrough simulation, we showed that wgLASSO can achieve better performance in building biologically relevant networks than purely data-driven models (e.g., neighbor selection, graphical LASSO), even when only a moderate level of information is available as prior biological knowledge. We evaluated the performance of dwgLASSO for survival time prediction using two microarray breast cancer datasets previously reported by Bild et al. and van de Vijver et al. Compared with the top 10 significant genes selected by conventional differential gene expression analysis method, the top 10 significant genes selected by dwgLASSO in the dataset from Bild et al. led to a significantly improved survival time prediction in the independent dataset from van de Vijver et al. Among the 10 genes selected by dwgLASSO, UBE2S, SALL2, XBP1 and KIAA0922 have been confirmed by literature survey to be highly relevant in breast cancer biomarker discovery study. Additionally, we tested dwgLASSO on TCGA RNA-seq data acquired from patients with hepatocellular carcinoma (HCC) on tumors samples and their corresponding non-tumorous liver tissues. Improved sensitivity, specificity and area under curve (AUC) were observed when comparing dwgLASSO with conventional differential gene expression analysis method.ConclusionsThe proposed network-based differential gene expression analysis algorithm dwgLASSO can achieve better performance than conventional differential gene expression analysis methods by integrating information at both gene expression and network topology levels. The incorporation of prior biological knowledge can lead to the identification of biologically meaningful genes in cancer biomarker studies.
| S-EPMC5303311 | biostudies-literature
Project description:MotivationDifferential network inference is a fundamental and challenging problem to reveal gene interactions and regulation relationships under different conditions. Many algorithms have been developed for this problem; however, they do not consider the differences between the importance of genes, which may not fit the real-world situation. Different genes have different mutation probabilities, and the vital genes associated with basic life activities have less fault tolerance to mutation. Equally treating all genes may bias the results of differential network inference. Thus, it is necessary to consider the importance of genes in the models of differential network inference.ResultsBased on the Gaussian graphical model with adaptive gene importance regularization, we develop a novel Importance-Penalized Joint Graphical Lasso method (IPJGL) for differential network inference. The presented method is validated by the simulation experiments as well as the real datasets. Furthermore, to precisely evaluate the results of differential network inference, we propose a new metric named APC2 for the differential levels of gene pairs. We apply IPJGL to analyze the TCGA colorectal and breast cancer datasets and find some candidate cancer genes with significant survival analysis results, including SOST for colorectal cancer and RBBP8 for breast cancer. We also conduct further analysis based on the interactions in the Reactome database and confirm the utility of our method.Availability and implementationR source code of Importance-Penalized Joint Graphical Lasso is freely available at https://github.com/Wu-Lab/IPJGL.Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC8756181 | biostudies-literature
Project description:Co-expression network analysis provides useful information for studying gene regulation in biological processes. Examining condition-specific patterns of co-expression can provide insights into the underlying cellular processes activated in a particular condition. One challenge in this type of analysis is that the sample sizes in each condition are usually small, making the statistical inference of co-expression patterns highly underpowered. A joint network construction that borrows information from related structures across conditions has the potential to improve the power of the analysis. One possible approach to constructing the co-expression network is to use the Gaussian graphical model. Though several methods are available for joint estimation of multiple graphical models, they do not fully account for the heterogeneity between samples and between co-expression patterns introduced by condition specificity. Here we develop the condition-adaptive fused graphical lasso (CFGL), a data-driven approach to incorporate condition specificity in the estimation of co-expression networks. We show that this method improves the accuracy with which networks are learned. The application of this method on a rat multi-tissue dataset and The Cancer Genome Atlas (TCGA) breast cancer dataset provides interesting biological insights. In both analyses, we identify numerous modules enriched for Gene Ontology functions and observe that the modules that are upregulated in a particular condition are often involved in condition-specific activities. Interestingly, we observe that the genes strongly associated with survival time in the TCGA dataset are less likely to be network hubs, suggesting that genes associated with cancer progression are likely to govern specific functions or execute final biological functions in pathways, rather than regulating a large number of biological processes. Additionally, we observed that the tumor-specific hub genes tend to have few shared edges with normal tissue, revealing tumor-specific regulatory mechanism.
| S-EPMC6173447 | biostudies-literature
Project description:Gene set testing is an important bioinformatics technique that addresses the challenges of power, interpretation and replication. To better support the analysis of large and highly overlapping gene set collections, researchers have recently developed a number of multiset methods that jointly evaluate all gene sets in a collection to identify a parsimonious group of functionally independent sets. Unfortunately, current multiset methods all use binary indicators for gene and gene set activity and assume that a gene is active if any containing gene set is active. This simplistic model limits performance on many types of genomic data. To address this limitation, we developed gene set Selection via LASSO Penalized Regression (SLPR), a novel mapping of multiset gene set testing to penalized multiple linear regression. The SLPR method assumes a linear relationship between continuous measures of gene activity and the activity of all gene sets in the collection. As we demonstrate via simulation studies and the analysis of TCGA data using MSigDB gene sets, the SLPR method outperforms existing multiset methods when the true biological process is well approximated by continuous activity measures and a linear association between genes and gene sets.
| S-EPMC5499546 | biostudies-literature
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: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.
| S-EPMC4307846 | biostudies-literature
Project description:In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.
| S-EPMC7845917 | biostudies-literature
Project description:Inferring gene co-expression networks is a useful process for understanding gene regulation and pathway activity. The networks are usually undirected graphs where genes are represented as nodes and an edge represents a significant co-expression relationship. When expression data of multiple (p) genes in multiple (K) conditions (e.g., treatments, tissues, strains) are available, joint estimation of networks harnessing shared information across them can significantly increase the power of analysis. In addition, examining condition-specific patterns of co-expression can provide insights into the underlying cellular processes activated in a particular condition. Condition adaptive fused graphical lasso (CFGL) is an existing method that incorporates condition specificity in a fused graphical lasso (FGL) model for estimating multiple co-expression networks. However, with computational complexity of O(p2K log K), the current implementation of CFGL is prohibitively slow even for a moderate number of genes and can only be used for a maximum of three conditions. In this paper, we propose a faster alternative of CFGL named rapid condition adaptive fused graphical lasso (RCFGL). In RCFGL, we incorporate the condition specificity into another popular model for joint network estimation, known as fused multiple graphical lasso (FMGL). We use a more efficient algorithm in the iterative steps compared to CFGL, enabling faster computation with complexity of O(p2K) and making it easily generalizable for more than three conditions. We also present a novel screening rule to determine if the full network estimation problem can be broken down into estimation of smaller disjoint sub-networks, thereby reducing the complexity further. We demonstrate the computational advantage and superior performance of our method compared to two non-condition adaptive methods, FGL and FMGL, and one condition adaptive method, CFGL in both simulation study and real data analysis. We used RCFGL to jointly estimate the gene co-expression networks in different brain regions (conditions) using a cohort of heterogeneous stock rats. We also provide an accommodating C and Python based package that implements RCFGL.
| S-EPMC9821764 | biostudies-literature
Project description:MotivationGraphical lasso (Glasso) is a widely used tool for identifying gene regulatory networks in systems biology. However, its computational efficiency depends on the choice of regularization parameter (tuning parameter), and selecting this parameter can be highly time consuming. Although fully Bayesian implementations of Glasso alleviate this problem somewhat by specifying a priori distribution for the parameter, these approaches lack the scalability of their frequentist counterparts.ResultsHere, we present a new Monte Carlo Penalty Selection method (MCPeSe), a computationally efficient approach to regularization parameter selection for Glasso. MCPeSe combines the scalability and low computational cost of the frequentist Glasso with the ability to automatically choose the regularization by Bayesian Glasso modeling. MCPeSe provides a state-of-the-art 'tuning-free' model selection criterion for Glasso and allows exploration of the posterior probability distribution of the tuning parameter.Availability and implementationR source code of MCPeSe, a step by step example showing how to apply MCPeSe and a collection of scripts used to prepare the material in this article are publicly available at GitHub under GPL (https://github.com/markkukuismin/MCPeSe/).Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC8097680 | biostudies-literature