scholarly journals Beyond Lasso: A Survey of Nonconvex Regularization in Gaussian Graphical Models

2020 ◽  
Author(s):  
Donald Ray Williams
Keyword(s):  
Model Selection ◽  
Graphical Models ◽  
Graphical Model ◽  
Tuning Parameter ◽  
Future Research ◽  
Dependence Structure ◽  
Post Traumatic Stress ◽  
Absolute Deviation ◽  
Oracle Properties ◽  
Nonconvex Regularization

Studying complex relations in multivariate datasets is a common task in psychological science. 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 across the sciences, 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, this information has not been synthesized. This paper provides a comprehensive survey of nonconvex regularization that spans from the smoothly clipped absolute deviation penalty to continuous approximations of the $\ell_0$-penalty (i.e., best subset) for directly estimating the inverse covariance matrix. A common thread shared by these penalties is that they all enjoy the oracle properties, that is, they perform as though the \emph{true} generating model were known in advance. To ensure their theoretical properties are general, I conducted extensive numerical experiments that indicated superior and more than competitive performance when compared to glasso and non-regularized model selection, respectively, all the while being computationally feasible for many variables. In addition, the important topics of tuning parameter selection and statistical inference in regularized models are reviewed.The penalties are employed to estimate the dependence structure of post-traumatic stress disorder symptoms. The discussion includes several ideas for future research, including a plethora of information to facilitate their study. I have implemented the methods in the

scholarly journals Sparse Graphical Models for Functional Connectivity Networks: Best Methods and the Autocorrelation Issue

2017 ◽  
Author(s):  
Yunan Zhu ◽  
Ivor Cribben
Keyword(s):  
Graphical Models ◽  
Graphical Model ◽  
Brain Networks ◽  
Information Criterion ◽  
Selection Method ◽  
Absolute Deviation ◽  
Data Set ◽  
Functional Brain ◽  
Functional Brain Networks ◽  
The Impact

AbstractSparse graphical models are frequently used to explore both static and dynamic functional brain networks from neuroimaging data. However, the practical performance of the models has not been studied in detail for brain networks. In this work, we have two objectives. First, we compare several sparse graphical model estimation procedures and several selection criteria under various experimental settings, such as different dimensions, sample sizes, types of data, and sparsity levels of the true model structures. We discuss in detail the superiority and deficiency of each combination. Second, in the same simulation study, we show the impact of autocorrelation and whitening on the estimation of functional brain networks. We apply the methods to a resting-state functional magnetic resonance imaging (fMRI) data set. Our results show that the best sparse graphical model, in terms of detection of true connections and having few false-positive connections, is the smoothly clipped absolute deviation (SCAD) estimating method in combination with the Bayesian information criterion (BIC) and cross-validation (CV) selection method. In addition, the presence of autocorrelation in the data adversely affects the estimation of networks but can be helped by using the CV selection method. These results question the validity of a number of fMRI studies where inferior graphical model techniques have been used to estimate brain networks.

scholarly journals Gap-com: General model selection criterion for sparse undirected gene networks with non-trivial community structure

2021 ◽  
Author(s):  
Markku Kuismin ◽  
Fatemeh Dodangeh ◽  
Mikko J Sillanpää
Keyword(s):  
Model Selection ◽  
Graphical Models ◽  
Network Structure ◽  
Gene Networks ◽  
Gene Network ◽  
Graphical Model ◽  
Regularization Parameter ◽  
Selection Criterion ◽  
Biological Data ◽  
Model Selection Criterion

Abstract We introduce a new model selection criterion for sparse complex gene network modeling where gene co-expression relationships are estimated from data. This is a novel formulation of the gap statistic and it can be used for the optimal choice of a regularization parameter in graphical models. Our criterion favors gene network structure which differs from a trivial gene interaction structure obtained totally at random. We call the criterion the gap-com statistic (gap community statistic). The idea of the gap-com statistic is to examine the difference between the observed and the expected counts of communities (clusters) where the expected counts are evaluated using either data permutations or reference graph (the Erdős-Rényi graph) resampling. The latter represents a trivial gene network structure determined by chance. We put emphasis on complex network inference because the structure of gene networks is usually non-trivial. For example, some of the genes can be clustered together or some genes can be hub genes. We evaluate the performance of the gap-com statistic in graphical model selection and compare its performance to some existing methods using simulated and real biological data example.

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 Impact of World Trade Center-Related Health Research: An Application of the NIEHS Translational Framework

2021 ◽  
Vol 18 (5) ◽  
pp. 2659
Author(s):  
Jaime Madrigano ◽  
Thomas W. Concannon ◽  
Sean Mann ◽  
Sameer M. Siddiqi ◽  
Ramya Chari ◽  
...  
Keyword(s):  
World Trade ◽  
Grey Literature ◽  
World Trade Center ◽  
Diagnostic Procedures ◽  
Health Conditions ◽  
Future Research ◽  
Physical And Mental Health ◽  
Post Traumatic Stress ◽  
Related Research ◽  
Trade Center

The World Trade Center Health Program (WTCHP) has a research mission to identify physical and mental health conditions that may be related to the 9/11 terrorist attacks as well as effective diagnostic procedures and treatments for WTC-related health conditions. The ability of the WTCHP to serve its members and realize positive impacts on all of its stakeholders depends on effective translation of research findings. As part of an ongoing assessment of the translational impact of World Trade Center (WTC)-related research, we applied the National Institute of Environmental Health Sciences (NIEHS) translational framework to two case studies: WTC-related research on post-traumatic stress disorder (PTSD) and cancer. We conducted a review of 9/11 health-related research in the peer-reviewed literature through October 2017, grey literature, and WTCHP program documentation. We mapped peer-reviewed studies in the literature to the NIEHS framework and used WTCHP program documentation and grey literature to find evidence of translation of research into clinical practice and policy. Using the NIEHS framework, we identified numerous translational milestones and bridges, as well as areas of opportunity, within each case study. This application demonstrates the utility of the NIEHS framework for documenting progress toward public health impact and for setting future research goals.

scholarly journals Integrating additional knowledge into the estimation of graphical models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yunqi Bu ◽  
Johannes Lederer
Keyword(s):  
Graphical Models ◽  
Tuning Parameter ◽  
Functional Magnetic Resonance ◽  
Resonance Imaging ◽  
Graphical Modeling ◽  
Standard Methods ◽  
Neighborhood Selection ◽  
Selection For ◽  
The Brain

Abstract Graphical models such as brain connectomes derived from functional magnetic resonance imaging (fMRI) data are considered a prime gateway to understanding network-type processes. We show, however, that standard methods for graphical modeling can fail to provide accurate graph recovery even with optimal tuning and large sample sizes. We attempt to solve this problem by leveraging information that is often readily available in practice but neglected, such as the spatial positions of the measurements. This information is incorporated into the tuning parameter of neighborhood selection, for example, in the form of pairwise distances. Our approach is computationally convenient and efficient, carries a clear Bayesian interpretation, and improves standard methods in terms of statistical stability. Applied to data about Alzheimer’s disease, our approach allows us to highlight the central role of lobes in the connectivity structure of the brain and to identify an increased connectivity within the cerebellum for Alzheimer’s patients compared to other subjects.

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 Treatment of adult post-traumatic stress disorder using a future-oriented writing therapy approach

2009 ◽  
Vol 2 (4) ◽  
pp. 243-255 ◽  
Author(s):  
Reginald D. V. Nixon ◽  
Leonard W. Kling
Keyword(s):  
Post Traumatic Stress Disorder ◽  
Traumatic Stress ◽  
Expressive Writing ◽  
Stress Disorder ◽  
Post Treatment ◽  
Future Research ◽  
Post Traumatic Stress ◽  
Post Traumatic ◽  
Ptsd Severity

AbstractThe aim of this pilot study was to test whether a future-oriented expressive writing intervention is able to reduce post-traumatic stress disorder (PTSD) severity and associated symptoms such as depression and unhelpful trauma-related beliefs. In an uncontrolled pre-/ post-design participants attended 8 weeks of manualized therapy. Assessment was undertaken pre- and post-treatment, and participants also completed a 3-month follow-up assessment. Of the 17 participants who began therapy, 13 were treatment completers. Results indicated a significant decrease in PTSD severity, depression and unhelpful trauma-related cognitions from pre- to post-treatment and at 3-month follow-up. Clinically meaningful change was more modest; however, three participants reported PTSD remission at 3-month follow-up. It is concluded that expressive writing with a focus on achieving future goals and personal change may have some utility in reducing post-traumatic stress but future research will need to investigate this with greater methodological rigour before firm conclusions can be made.

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