scholarly journals GGMncv: Nonconvex Penalized Gaussian Graphical Models in R

2020 ◽  
Author(s):  
Donald Ray Williams
Keyword(s):  
Graphical Models ◽  
Graphical Model ◽  
Dependence Structure ◽  
Penalized Least Squares ◽  
Gaussian Graphical Model ◽  
Gaussian Graphical Models ◽  
Personality Psychology ◽  
Conditional Dependence ◽  
Graphical Lasso ◽  
Common Task

Studying complex relations in multivariate datasets is a common task across the sciences. Recently, the Gaussian graphical model has emerged as an increasingly popular model for characterizing the conditional dependence structure of random variables. Although the graphical lasso ($\ell_1$-regularization) is the most well-known estimator, it has several drawbacks that make it less than ideal for model selection. There are now alternative forms of regularization that were developed specifically to overcome issues inherent to the $\ell_1$-penalty.To date, however, these alternatives have been slow to work their way into software for research workers. To address this dearth of software, I developed the package \textbf{GGMncv} that includes a variety of nonconvex penalties, two algorithms for their estimation, plotting capabilities, and an approach for making statistical inference. As an added bonus, \textbf{GGMncv} can be used for nonconvex penalized least squares. After describing the various nonconvex penalties, the functionality of \textbf{GGMncv} is demonstrated through examples using a dataset from personality psychology.

scholarly journals GGMnonreg: Non-Regularized Gaussian Graphical Models in R

2021 ◽  
Author(s):  
Donald Ray Williams
Keyword(s):  
Graphical Models ◽  
Brain Connectivity ◽  
Dependence Structure ◽  
Gaussian Graphical Models ◽  
Graphical Modeling ◽  
Conditional Dependence ◽  
Common Task ◽  
The Social ◽  
Cortical Regions ◽  
Low Dimensional

Studying complex relations in multivariate datasets is a common task across the sciences. Cognitive neuroscientists model brain connectivity with the goal of unearthing functional and structural associations betweencortical regions. In clinical psychology, researchers wish to better understand the intri-cate web of symptom interrelations that underlie mental health disorders. To this end, graphical modeling has emerged as an oft-used tool in the chest of scientific inquiry. Thebasic idea is to characterize multivariate relations by learning the conditional dependence structure. The cortical regions or symptoms are nodes and the featured connections linking nodes are edges that graphically represent the conditional dependence structure. Graphical modeling is quite common in fields with wide data, that is, when there are more variables (p) thanobservations (n). Accordingly, many regularization-based approaches have been developed for those kinds of data. More recently, graphical modeling has emerged in psychology, where the data is typically long or low-dimensional. The primary purpose of GGMnonreg is to provide methods that were specifically designed for low-dimensional data (e.g., those common in the social-behavioral sciences), for which there is a dearth of methodology.

Comparison of two inference approaches in Gaussian graphical models

2017 ◽  
Vol 42 (2) ◽  
Author(s):  
Vilda Purutçuoğlu ◽  
Ezgi Ayyıldız ◽  
Ernst Wit
Keyword(s):  
Graphical Models ◽  
Gradient Descent ◽  
Probabilistic Models ◽  
Graphical Model ◽  
Computational Cost ◽  
Area Under The Curve ◽  
Gaussian Graphical Model ◽  
Gaussian Graphical Models ◽  
Graphical Lasso ◽  
Conditional Independency

AbstractIntroduction:The Gaussian Graphical Model (GGM) is one of the well-known probabilistic models which is based on the conditional independency of nodes in the biological system. Here, we compare the estimates of the GGM parameters by the graphical lasso (glasso) method and the threshold gradient descent (TGD) algorithm.Methods:We evaluate the performance of both techniques via certain measures such as specificity, F-measure and AUC (area under the curve). The analyses are conducted by Monte Carlo runs under different dimensional systems.Results:The results indicate that the TGD algorithm is more accurate than the glasso method in all selected criteria, whereas, it is more computationally demanding than this method too.Discussion and conclusion:Therefore, in high dimensional systems, we recommend glasso for its computational efficiency in spite of its loss in accuracy and we believe than the computational cost of the TGD algorithm can be improved by suggesting alternative steps in inference of the network.

scholarly journals Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽  
2020 ◽  
Author(s):  
S Na ◽  
M Kolar ◽  
O Koyejo
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Statistical Error ◽  
Real Data ◽  
Low Rank ◽  
Conditional Dependence ◽  
Gradient Descent Algorithm ◽  
The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

scholarly journals Bayesian Uncertainty Estimation for Gaussian Graphical Models and Centrality Indices

2021 ◽  
Author(s):  
Joran Jongerling ◽  
Sacha Epskamp ◽  
Donald Ray Williams
Keyword(s):  
Bayesian Estimation ◽  
Graphical Models ◽  
Estimation Methods ◽  
Centrality Measures ◽  
Gaussian Graphical Models ◽  
Graphical Lasso ◽  
Study Results ◽  
Partial Correlations ◽  
Good Coverage ◽  
Better Than

Gaussian Graphical Models (GGMs) are often estimated using regularized estimation and the graphical LASSO (GLASSO). However, the GLASSO has difficulty estimating(uncertainty in) centrality indices of nodes. Regularized Bayesian estimation might provide a solution, as it is better suited to deal with bias in the sampling distribution ofcentrality indices. This study therefore compares estimation of GGMs with a Bayesian GLASSO- and a Horseshoe prior to estimation using the frequentist GLASSO in an extensive simulation study. Results showed that out of the two Bayesian estimation methods, the Bayesian GLASSO performed best. In addition, the Bayesian GLASSOperformed better than the frequentist GLASSO with respect to bias in edge weights, centrality measures, correlation between estimated and true partial correlations, andspecificity. With respect to sensitivity the frequentist GLASSO performs better.However, sensitivity of the Bayesian GLASSO is close to that of the frequentist GLASSO (except for the smallest N used in the simulations) and tends to be favored over the frequentist GLASSO in terms of F1. With respect to uncertainty in the centrality measures, the Bayesian GLASSO shows good coverage for strength andcloseness centrality. Uncertainty in betweenness centrality is estimated less well, and typically overestimated by the Bayesian GLASSO.

scholarly journals On Formalizing Theoretical Expectations: Bayesian Testing of Central Structures in Psychological Networks

2020 ◽  
Author(s):  
Josue E. Rodriguez ◽  
Donald Ray Williams ◽  
Philippe Rast ◽  
Joris Mulder
Keyword(s):  
Hypothesis Testing ◽  
Graphical Models ◽  
Network Theory ◽  
Dependence Structure ◽  
Gaussian Graphical Models ◽  
Psychological Constructs ◽  
Partial Correlations ◽  
Psychopathology Symptom ◽  
The Rich ◽  
Cohesive Framework

Network theory has emerged as a popular framework for conceptualizing psychological constructs and mental disorders. Initially, network analysis was motivated in part by the thought that it can be used for hypothesis generation. Although the customary approach for network modeling is inherently exploratory, we argue that there is untapped potential for confirmatory hypothesis testing. In this work, we bring to fruition the potential of Gaussian graphical models for generating testable hypotheses. This is accomplished by merging exploratory and confirmatory analyses into a cohesive framework built around Bayesian hypothesis testing of partial correlations. We first present a motivating example based on a customary, exploratory analysis, where it is made clear how information encoded by the conditional (in)dependence structure can be used to formulate hypotheses. Building upon this foundation, we then provide several empirical examples that unify exploratory and confirmatory testing in psychopathology symptom networks. In particular, we (1) estimate exploratory graphs; (2) derive hypotheses based on the most central structures; and (3) test those hypotheses in a confirmatory setting. Our confirmatory results uncovered an intricate web of relations, including an order to edge weights within comorbidity networks. This illuminates the rich and informative inferences that can be drawn with the proposed approach. We conclude with recommendations for applied researchers, in addition to discussing how our methodology answers recent calls to begin developing formal models related to the conditional (in)dependence structure of psychological networks.

scholarly journals Joint Microbial and Metabolomic Network Estimation with the Censored Gaussian Graphical Model

2020 ◽  
Author(s):  
Jing Ma
Keyword(s):  
Graphical Model ◽  
Association Studies ◽  
Joint Analysis ◽  
Gaussian Graphical Model ◽  
Model Framework ◽  
Data Set ◽  
Conditional Dependence ◽  
Metabolomic Data ◽  
Network Estimation ◽  
Microbiome Data

Abstract Joint analysis of microbiome and metabolomic data represents an imperative objective as the field moves beyond basic microbiome association studies and turns towards mechanistic and translational investigations. We present a censored Gaussian graphical model framework, where the metabolomic data are treated as continuous and the microbiome data as censored at zero, to identify direct interactions (defined as conditional dependence relationships) between microbial species and metabolites. Simulated examples show that our method metaMint performs favorably compared to the existing ones. metaMint also provides interpretable microbe-metabolite interactions when applied to a bacterial vaginosis data set. R implementation of metaMint is available on GitHub.

scholarly journals Joint Microbial and Metabolomic Network Estimation with the Censored Gaussian Graphical Model

2020 ◽  
Author(s):  
Jing Ma
Keyword(s):  
Graphical Model ◽  
Association Studies ◽  
Joint Analysis ◽  
Gaussian Graphical Model ◽  
Model Framework ◽  
Data Set ◽  
Conditional Dependence ◽  
Metabolomic Data ◽  
Network Estimation ◽  
Microbiome Data

AbstractJoint analysis of microbiome and metabolomic data represents an imperative objective as the field moves beyond basic microbiome association studies and turns towards mechanistic and translational investigations. We present a censored Gaussian graphical model framework, where the metabolomic data are treated as continuous and the microbiome data as censored at zero, to identify direct interactions (defined as conditional dependence relationships) between microbial species and metabolites. Simulated examples show that our method metaMint performs favorably compared to existing ones. metaMint also provides interpretable microbe-metabolite interactions when applied to a bacterial vaginosis data set. R implementation of metaMint is available on GitHub.

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