Gaussian Graphical Models Research Articles

SEMbap: Bow-free covariance search and data de-correlation.

Large-scale studies of gene expression are commonly influenced by biological and technical sources of expression variation, including batch effects, sample characteristics, and environmental impacts. Learning the causal relationships between observable variables may be challenging in the presence of unobserved confounders. Furthermore, many high-dimensional regression techniques may perform worse. In fact, controlling for unobserved confounding variables is essential, and many deconfounding methods have been suggested for application in a variety of situations. The main contribution of this article is the development of a two-stage deconfounding procedure based on Bow-free Acyclic Paths (BAP) search developed into the framework of Structural Equation Models (SEM), called SEMbap(). In the first stage, an exhaustive search of missing edges with significant covariance is performed via Shipley d-separation tests; then, in the second stage, a Constrained Gaussian Graphical Model (CGGM) is fitted or a low dimensional representation of bow-free edges structure is obtained via Graph Laplacian Principal Component Analysis (gLPCA). We compare four popular deconfounding methods to BAP search approach with applications on simulated and observed expression data. In the former, different structures of the hidden covariance matrix have been replicated. Compared to existing methods, BAP search algorithm is able to correctly identify hidden confounding whilst controlling false positive rate and achieving good fitting and perturbation metrics.

Joint estimation for multisource Gaussian graphical models based on transfer learning

This study considers data from multiple sources for Gaussian graphical models with one target graph and several auxiliary graphs. We propose a method called joint estimation for multisource Gaussian graphical models (JEM-GGM) to achieve a stable and accurate estimate of the target graph. Using the information from the auxiliary graphs, the proposed method is used to effectively solve the problem of small sample sizes. In this method, equivalent regression models are developed for graphs and the difference between the auxiliary and target graphs was penalized to ensure computational efficiency and improve estimation accuracy. Simulations revealed that the proposed method always outperformed other methods in terms of estimation and prediction accuracy. The application of this method to breast and lymphatic cancer cell lines reveals that the proposed method always obtains a sparse collection of important genome pairs.

Irruption of Network Analysis to Explain Dietary, Psychological and Nutritional Patterns and Metabolic Health Status in Metabolically Healthy and Unhealthy Overweight and Obese University Students: Ecuadorian Case.

The association between dietary nutritional patterns, psychological factors, and metabolic health status has not been investigated in university students. There are studies that include numerous variables to test hypotheses from various theoretical bases, but due to their complexity, they have not been studied in combination. The scientific community recognizes the use of Gaussian graphical models (GGM) as a set of novel methods capable of addressing this. To apply GGMs to derive specific networks for groups of healthy and unhealthy obese individuals that represent nutritional, psychological, and metabolic patterns in an Ecuadorian population. This was a quantitative, non-experimental, cross-sectional, correlational study conducted on a sample of 230 obese/overweight university students, selected through a multi-stage random sampling method. To assess usual dietary intake, a Food Frequency Questionnaire (FFQ) was used; to evaluate psychological profiles (anxiety, depression, and stress), the DASS-21 scale was employed; blood pressure and anthropometric data were collected; and insulin levels, lipid profiles, and glucose levels were determined using fasting blood samples. The International Diabetes Federation (IDF) criteria were applied to identify metabolically healthy and unhealthy individuals. Statistical analysis relied on univariate methods (frequencies, measures of central tendency, and dispersion), and the relationships were analyzed through networks. The Mann-Whitney U test was used to analyze differences between groups. In metabolically unhealthy obese individuals, GGMs identified a primary network consisting of the influence of waist circumference on blood pressure and insulin levels. In the healthy obese group, a different network was identified, incorporating stress and anxiety variables that influenced blood pressure, anthropometry, and insulin levels. Other identified networks show the dynamics of obesity and the effect of waist circumference on triglycerides, anxiety, and riboflavin intake. GGMs are an exploratory method that can be used to construct networks that illustrate the behavior of obesity in the studied population. In the future, the identified networks could form the basis for updating obesity management protocols in Primary Care Units and supporting clinical interventions in Ecuador.

Topological properties of psychopathological networks of healthy and disordered individuals across mental disorders

The identification of psychopathological markers has been the focus of several scientific fields. The results were inconsistent due to lack of a clear nosology. Network analysis, focusing on the interactions between symptoms, provided important insights into the nosology of mental disorders. These interactions originate several topological properties that could constitute markers of psychopathology. One of these properties is network connectivity, which has been explored in recent years. However, the results have been inconsistent, and the topological properties of psychopathological networks remain largely unexplored and unknown. We compared several topological properties (i.e., connectivity, average path length, assortativity, average degree, modularity, global clustering) of psychopathological networks of healthy and disordered participants across depression (N = 2830), generalized anxiety (N = 13,463), social anxiety (N = 12,814), and obsessive-compulsive disorder (N = 16,426). Networks were estimated using Bayesian Gaussian Graphical Models. The Janson-Shannon measure of divergence was used to identify differences between the network properties. Network connectivity distinguished healthy and disordered participants' networks in all disorders. However, in depression and generalized anxiety, network connectivity was higher in healthy participants. The presence and number of motifs also distinguished the networks of healthy and disordered participants. Other topological properties (i.e., modularity, clustering, average path length and average degree) seem to be disorder-specific. The psychopathological significance of network connectivity must be clarified. Some topological properties of psychopathological networks are promising markers of psychopathology and may contribute to clarifying the nosology of mental disorders.

Pathways to experienced coercion during psychiatric admission: a network analysis

BackgroundIn mental health care, experienced coercion, also known as perceived coercion, is defined as the patient’s subjective experience of being submitted to coercion. Besides formal coercion, many other factors have been identified as potentially affecting the experience of being coerced. This study aimed to explore the interplay between these factors and to provide new insights into how they lead to experienced coercion.MethodsCross-sectional network analysis was performed on data collected from 225 patients admitted to six psychiatric hospitals. Thirteen variables were selected and included in the analyses. A Gaussian Graphical Model (GGM) using Spearman’s rank-correlation method and EBICglasso regularisation was estimated. Centrality indices of strength and expected influence were computed. To evaluate the robustness of the estimated parameters, both edge-weight accuracy and centrality stability were investigated.ResultsThe estimated network was densely connected. Formal coercion was only weakly associated with both experienced coercion at admission and during hospital stay. Experienced coercion at admission was most strongly associated with the patients’ perceived level of implication in the decision-making process. Experienced humiliation and coercion during hospital stay, the most central node in the network, was found to be most strongly related to the interpersonal separation that patients perceived from staff, the level of coercion perceived upon admission and their satisfaction with the decision taken and the level of information received.ConclusionsReducing formal coercion may not be sufficient to effectively reduce patients’ feeling of being coerced. Different factors seemed indeed to come into play and affect experienced coercion at different stages of the hospitalisation process. Interventions aimed at reducing experienced coercion and its negative effects should take these stage-specific elements into account and propose tailored strategies to address them.

A Network Analysis of the Relationship Between Automation and Job Characteristics

The purpose of this study is to identify core occupational characteristics that affect the potential for a job to be automated and to reveal the relationship and paths between those characteristics, such as skill(s), work environment and knowledge. In this study, a network was estimated and visualised to identify the relationship between occupational characteristics using the Gaussian graphical model method and to reveal the occupational characteristics linked to the potential for automation variable. As a result of estimating and visualising the network, it was found that the occupational characteristics with low potential for automation were art, decision-making, assisting and caring for others and working in cramped spaces, while those with high potential for automation involved repeating the same tasks. Furthermore, after analysing the shortest paths from each occupational characteristic node to the automation node, it was revealed that even occupational characteristics with high potential for automation can have varying levels of automation possibility depending on the mediators. Based on the results, education and vocational training policies for low- and middle-skill workers, young workers and potential workers are suggested.

Gene co-expression network analysis for porcine intramuscular fatty acid composition

In pigs, meat quality depends markedly on the fatty acid (FA) content and composition of the intramuscular fat, which is partly determined by the gene expression in this tissue. The aim of this work was to identify the link between muscle gene expression and its FA composition. In an (Iberian × Duroc) × Duroc backcrossed pig population, we identified modules of co-expressed genes, and correlation analyses were performed for each of them versus the phenotypes, finding four relevant modules. Two of the modules were positively correlated with saturated FAs (SFAs) and monounsaturated FAs (MUFAs), while negatively correlated with polyunsaturated FAs (PUFAs) and the omega-6/omega-3 ratio. The gene-enrichment analysis showed that these modules had over-representation of pathways related with the biosynthesis of unsaturated FAs, the Peroxisome proliferator-activated receptor signalling pathway and FA elongation. The two other relevant modules were positively correlated with PUFA and the n-6/n-3 ratio, but negatively correlated with SFA and MUFA. In this case, they had an over-representation of pathways related with fatty and amino acid degradation, and with oxidative phosphorylation. Using a graphical Gaussian model, we inferred a network of connections between the genes within each module. The first module had 52 genes with 87 connections, and the most connected genes were ADIPOQ, which is related with FA oxidation, and ELOVL6 and FABP4, both involved in FA metabolism. The second module showed 196 genes connected by 263 edges, being FN1 and MAP3K11 the most connected genes. On the other hand, the third module had 161 genes connected by 251 edges and ATG13 was the top neighbouring gene, while the fourth module had 224 genes and 655 connections, and its most connected genes were related with mitochondrial pathways. Overall, this work successfully identified relevant muscle gene networks and modules linked with FA composition, providing further insights on how the physiology of the pigs influences FA composition.

Exploring the interconnections of anxiety, depression, sleep problems and health-promoting lifestyles among Chinese university students: a comprehensive network approach.

Anxiety, depression, and sleep problems are prevalent comorbid mental disorders among university students. The World Health Organization (WHO) emphasized a mental health promotion objective, recommending the consideration of protective health-promoting factors in strategies aimed at preventing mental disorders. Integrating theoretically significant constructs (such as protective factors) enhances our comprehension of the intricate mechanisms that underpin mental disorders. This study employed network analysis to first identify core and bridge symptoms within comorbid mental disorders and then explore how health-promoting lifestyles (HPLs) were associated with these disorders. The ultimate goal is to offer health promotion recommendations to enhance students' quality of life. A total of 3,896 qualified university students participated in this study. Anxiety, depression, sleep problems, and HPLs were assessed using the GAD-7, PHQ-9, PSQI, and HPLP-II scales. A Gaussian Graphical Model was used to construct the networks. The Network Comparison Test was applied to determine whether the associations between HPLs and comorbid symptoms vary by gender, educational level, family sibling, and mental health status. Low energy (PHQ4) had the highest strength centrality, followed by Daytime dysfunction (PSQI7) and Trouble relaxing (GAD4). Five bridge symptoms were identified: Daytime dysfunction (PSQI7), Self-harm even suicide (PHQ9), Sad mood (PHQ2), Low energy (PHQ4), and Feeling afraid (GAD7). Regarding protective HPLs, Physical activity, Spiritual growth, and Stress management generally emerged as the top three central mental health-promoting behaviors. Targeting core and bridge symptoms with timely and appropriate interventions can alleviate anxiety, depression, and sleep problems in this population. Moreover, promoting physical activity, fostering spiritual growth, and managing stress are likely to significantly enhance the overall mental health of university students.

The relation between mental health and career-related stress among prospective graduates in higher education stage during the COVID-19 pandemic: an evidence based on network analysis.

The outbreak of the COVID-19 pandemic has disrupted people's routine, bringing uncertainty and stress, leading to mental health issues. This situation is particularly acute among Chinese prospective graduates in higher education stage as they cannot predict the outcomes of their studies, graduation, and career development, and therefore experience career-related stress. This study included 4041 prospective graduates in higher education stage (using handy sampling) recruited in March 2020 as participants (M Age = 22.56, SD = 1.865), utilizing a Sparse Gaussian Graphical Model for regularized partial correlation network analysis of depression symptoms (by PHQ-9), anxiety symptoms (by GAD-7), and career-related stress, which aims to explore the role of career-related stress in the symptom networks of depression and anxiety among prospective graduates in their final semester. The results revealed that fatigue, sad mood, and psychomotor symptoms in depression, as well as uncontrollable worry and trouble relaxing in anxiety, were central symptoms in the network. Additionally, sad mood and guilt belonging to depressive symptoms, and feeling afraid, restlessness, and irritability belonging to anxiety symptoms, served as bridge symptoms connecting symptom communities. Specifically, guilt as a depressive symptom showed a strong association with employment stress in career-related stress. There were no significant differences in network structure and global strength based on participants' gender. However, despite no significant differences in network structure, the global strength of prospective graduates from Wuhan was significantly lower than samples from non-Hubei provinces, possibly indicative of a Typhoon Eye Effect. The findings of this study can inspire psychological professionals in higher education institutions to provide support for mental interventions and therapies for prospective graduates, and addressing career development issues.

Sleep, Mental Health, and the Need for Physical and Real-Life Social Contact with (Non-)Family Members during the COVID-19 Pandemic: A Bayesian Network Analysis.

Background/Objectives: The forced social isolation implemented to prevent the spread of the COVID-19 virus was accompanied by a worsening of mental health, an increase in insomnia symptoms, and the emergence of 'skin hunger'-an increased longing for personal touch. This study aimed to enhance our understanding of the interconnection between sleep, mental health, and the need for physical (NPC) and real-life social contact (NRL-SC). Methods: A total of 2827 adults participated in an online survey during the second COVID-19 lockdown. A Bayesian Gaussian copula graphical model (BGCGM) and a Bayesian-directed acyclic graph (DAG) were estimated, and mixed ANOVAs were carried out. Results: NPC with non-family members (t(2091) = 12.55, p < 0.001, d = 0.27) and relational lifestyle satisfaction (t(2089) = 13.62, p < 0.001, d = 0.30) were lower during the second lockdown than before the pandemic. In our BGCGM, there were weak positive edges between the need for PC and RL-SC on one hand and sleep and mental health on the other. Conclusions: During the second lockdown, people craved less physical contact with non-family members and were less satisfied with their relational lifestyle than before the pandemic. Individuals with a greater need for PC and RL-SC reported poorer mental health (i.e., worry, depression, and mental fatigue).

Heterogeneous latent transfer learning in Gaussian graphical models.

Gaussian graphical models (GGMs) are useful for understanding the complex relationships between biological entities. Transfer learning can improve the estimation of GGMs in a target dataset by incorporating relevant information from related source studies. However, biomedical research often involves intrinsic and latent heterogeneity within a study, such as heterogeneous subpopulations. This heterogeneity can make it difficult to identify informative source studies or lead to negative transfer if the source study is improperly used. To address this challenge, we developed a heterogeneous latent transfer learning (Latent-TL) approach that accounts for both within-sample and between-sample heterogeneity. The idea behind this approach is to "learn from the alike" by leveraging the similarities between source and target GGMs within each subpopulation. The Latent-TL algorithm simultaneously identifies common subpopulation structures among samples and facilitates the learning of target GGMs using source samples from the same subpopulation. Through extensive simulations and real data application, we have shown that the proposed method outperforms single-site learning and standard transfer learning that ignores the latent structures. We have also demonstrated the applicability of the proposed algorithm in characterizing gene co-expression networks in breast cancer patients, where the inferred genetic networks identified many biologically meaningful gene-gene interactions.

Insights from the nexus between economic growth and green energy

The research aims to provide a new approach and insights into the nexus between economic growth and green energy by analyzing their direct, indirect, and total linkages at the European Union level (EU-27). To this end, an advanced empirical analysis performed by network analysis, as Gaussian Graphical Models, is carried out for the period 2012–2022 The originality of network analysis lies in the fact that it allows the simultaneous visualization of all the links between variables in a complex system of dependencies. The novelty of the paper is twofold: first, it addresses the issue of renewable energy in an innovative way that captures three key stages of the EU policy (renewables’ capacity; share of renewable energy; and final consumption); second, it advances the nexus analysis by considering technological investments. Empirical results have validated the vital role of increasing the share of renewable energy in achieving sustainability and reducing greenhouse gas emissions. Also, the Research & Development and Gross Value added in environmental goods and services sector are found to positively influence sustainable development. The results are useful for policymakers and managers of organizations to understand the relationships between these variables better and thus, achieve climate neutrality.

SingleCellGGM enables gene expression program identification from single-cell transcriptomes and facilitates universal cell label transfer

Gene co-expression analysis of single-cell transcriptomes, aiming to define functional relationships between genes, is challenging due to excessive dropout values. Here, we developed a single-cell graphical Gaussian model (SingleCellGGM) algorithm to conduct single-cell gene co-expression network analysis. When applied to mouse single-cell datasets, SingleCellGGM constructed networks from which gene co-expression modules with highly significant functional enrichment were identified. We considered the modules as gene expression programs (GEPs). These GEPs enable direct cell-type annotation of individual cells without cell clustering, and they are enriched with genes required for the functions of the corresponding cells, sometimes at levels greater than 10-fold. The GEPs are conserved across datasets and enable universal cell-type label transfer across different studies. We also proposed a dimension-reduction method through averaging by GEPs for single-cell analysis, enhancing the interpretability of results. Thus, SingleCellGGM offers a unique GEP-based perspective to analyze single-cell transcriptomes and reveals biological insights shared by different single-cell datasets.

Algorithm 1045: A Covariate-Dependent Approach to Gaussian Graphical Modeling in R

Graphical models are used to capture complex multivariate relationships and have applications in diverse disciplines such as biology, physics, and economics. Within this field, Gaussian graphical models aim to identify the pairs of variables whose dependence is maintained even after conditioning on the remaining variables in the data, known as the conditional dependence structure of the data. There are many existing software packages for Gaussian graphical modeling, however, they often make restrictive assumptions that reduce their flexibility for modeling data that are not identically distributed. Conversely, covdepGE is an R implementation of a variational weighted pseudo-likelihood algorithm for modeling the conditional dependence structure as a continuous function of an extraneous covariate. To build on the efficiency of this algorithm, covdepGE leverages parallelism and C++ integration with R. Additionally, covdepGE provides fully-automated and data-driven hyperparameter specification while maintaining flexibility for the user to decide key components of the estimation procedure. Through an extensive simulation study spanning diverse settings, covdepGE is demonstrated to be top of its class in recovering the ground truth conditional dependence structure while efficiently managing computational overhead.

Psychological responses to the COVID-19 pandemic and situational impact: A network analysis in Hong Kong residents

BackgroundThe COVID-19 pandemic has had situational impacts and induced various psychological responses among residents. The present study aims to analyze the network structure of psychological responses to the pandemic and their relationships with situational impact, resilience, and well-being through a network approach. MethodsAn online survey recruited 1122 residents (mean age = 32.5 years, 65.4 % female) in Hong Kong from October 2020 to October 2021. The participants completed the Mental Impact and Distress Scale: Psychological Response (MIDc-PR) and other validated measures. Gaussian graphical modeling was conducted in R to identify the central MIDc-PR symptoms and their bridge linkages with situational impact, resilience, and well-being. ResultsIn the MIDc-PR network, the central symptoms were ‘Routine’ and ‘Images’ for Anticipation and ‘Tense’ and ‘Lonely’ for Modulation, with 12 bridge edges between the two clusters. In the combined network, the MIDc-PR nodes showed 12 bridge edges with situational impact, particularly in the health domain. ‘Concerned’, ‘Sleep’, and ‘Lonely’ showed negative linkages with resilience; ‘Unmotivated’ and ‘Trapped’ showed negative linkages with well-being. The network models showed good levels of stability and did not differ significantly in network structure and global strength across gender and age groups. LimitationsThe cross-sectional study design only allowed undirected associations in the network and could not model the within-subject effects. ConclusionsThe study findings contributed to the literature by elucidating the network structure of psychological responses to the pandemic. The central and bridge symptoms have clinical implications as potential targets for future interventions.

Predictive modelling of stress, anxiety and depression: A network analysis and machine learning study.

This study assessed predictors of stress, anxiety and depression during the COVID-19 pandemic using a large number of demographic, COVID-19 context and psychological variables. Data from 741 adults were drawn from the Boston College daily sleep and well-being survey. Baseline demographics, the long version of the daily surveys and the round one assessment of the survey were utilized for the present study. A Gaussian graphical model (GGM) was estimated as a feature selection technique on a subset of ordinal/continuous variables. An ensemble Random Forest (RF) machine learning algorithm was used for prediction. GGM was found to be an efficient feature selection method and supported the findings derived from the RF machine learning model. Psychological variables were significant predictors of stress, anxiety and depression, while demographic and COVID-19-related factors had minimal predictive value. The outcome variables were mutually predictive of each other, and negative affect and subjective sleep quality were the common predictors of these outcomes of stress, anxiety, and depression. The study identifies risk factors for adverse mental health outcomes during the pandemic and informs interventions to mitigate the impact on mental health.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

Unravelling inter-relations within and between psychodynamic constructs and psychopathology using network analysis.

Psychodynamic constructs and psychopathology are closely inter-related, but more detailed insight is needed. We investigated these complex inter-relations using network analysis. A Gaussian graphical model in a sample of N = 2232 psychotherapeutic inpatients was estimated. Self-administered questionnaires to assess interpersonal relations (Inventory of Interpersonal Problems-32), psychodynamic conflicts (Operationalized Psychodynamic Diagnosis-Conflict Questionnaire), personality functioning (Operationalized Psychodynamic Diagnosis-Structure Questionnaire-Short Form, Inventory of Personality Organization-Short Form), and psychopathology (Brief Symptom Inventory) were utilized. We investigated the network structure, identified the most inter-related psychodynamic constructs and the psychodynamic constructs with the strongest inter-relations to psychopathology, and explored the clustering of all included constructs. Active and passive conflict processing modes were negatively inter-related in most conflicts. Passive conflict processing modes were more strongly related to psychopathology than active ones in all conflicts, apart from the care versus autarky conflict. Identity diffusion shared the strongest inter-relations within psychodynamic constructs. The psychodynamic constructs that were most strongly related to psychopathology were impairments in self-perception and the passive self-worth conflict. Psychopathology and psychodynamic constructs formed distinct clusters. Our results emphasize the relevance of personality functioning within psychodynamic constructs and in relation to psychopathology.

On some algorithms for estimation in Gaussian graphical models

Abstract In Gaussian graphical models, the likelihood equations must typically be solved iteratively. This paper investigates two algorithms: a version of iterative proportional scaling, which avoids inversion of large matrices, and an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, which corresponds to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive-definite starting value to converge. We provide an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof of existence of the maximum likelihood estimator in such cases.

Gaussian Graphical Model Estimation and Selection for High-Dimensional Incomplete Data Using Multiple Imputation and Horseshoe Estimators

Gaussian Graphical Model Estimation and Selection for High-Dimensional Incomplete Data Using Multiple Imputation and Horseshoe Estimators