Gaussian Graphical Models Research Articles

A special contribution from spatial ability to math word problem solving: Evidence from structural equation modelling and network analysis

There is a growing body of research into the factors contributing to math word problem solving. However, these studies usually use limited number of potential predictors (precluding assessing of their contribution in comparison with other factors or “g” general intelligence) and some predictors (such as analogical and hypothetical reasoning) are largely omitted. Thus, the aim of the current study was to explore contributions of different types of reasoning to math word problem solving and whether these contributions have added value compared with each other and general cognitive ability. Chinese schoolchildren in Grades 3 (N = 199; Mage = 102.4 months), 4 (N = 162; Mage = 114.6), 5 (N = 174; Mage = 126.1) and 6 (N = 180; Mage = 138.6) completed 8 tasks tapping into spatial, mechanical, verbal, mathematic, hypothetical and analogical reasoning. Our data showed that when 6 general cognitive factors load onto General cognitive ability factor in a Structural Equation Model (SEM), only spatial visualization has additional contribution to Word problem solving factor. Gaussian Graphical models (GGMs) showed that 2 verbal tasks and spatial visualization showed stable (present in at least 3 out of 4 grades) contributions to both word problem solving tasks. Analogical reasoning showed contribution to Process of word problem solving only. To sum up, both SEM and GGMs converged on the importance of spatial ability for mathematical word problems solving. Our results call for verbal and spatial ability to be routinely assessed and targeted by educational interventions within maths curriculum.

On the application of Gaussian graphical models to paired data problems

Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointly learning their independence structures. We consider the case where there are exactly two dependent groups and the association structure is represented by a family of coloured Gaussian graphical models suited to deal with paired data problems. To learn the two dependent graphs, together with their across-graph association structure, we implement a fused graphical lasso penalty. We carry out a comprehensive analysis of this approach, with special attention to the role played by some relevant submodel classes. In this way, we provide a broad set of tools for the application of Gaussian graphical models to paired data problems. These include results useful for the specification of penalty values in order to obtain a path of lasso solutions and an ADMM algorithm that solves the fused graphical lasso optimization problem. Finally, we carry out a simulation study to compare our method with the traditional graphical lasso, and present an application of our method to cancer genomics where it is of interest to compare cancer cells with a control sample from histologically normal tissues adjacent to the tumor. All the methods described in this article are implemented in the R package pdglasso available at https://github.com/savranciati/pdglasso.

Multi-task Learning for Gaussian Graphical Regressions with High Dimensional Covariates

Gaussian graphical regression is a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which permits the response variables and covariates to outnumber the sample size. However, traditional approaches of fitting the model via separate node-wise lasso regressions overlook the network-induced structure among these regressions, leading to high error rates, particularly when the number of nodes is large. To address this issue, we propose a multi-task learning estimator for fitting Gaussian graphical regression models, which incorporates a cross-task group sparsity penalty and a within-task element-wise sparsity penalty to govern the sparsity of active covariates and their effects on the graph, respectively. We also develop an efficient augmented Lagrangian algorithm for computation, which solves subproblems with a semi-smooth Newton method. We further prove that our multi-task learning estimator has considerably lower error rates than the separate node-wise regression estimates, as the cross-task penalty enables borrowing information across tasks. We examine the utility of our method through simulations and an application to a gene co-expression network study with brain cancer patients.

Concentration of a Sparse Bayesian Model With Horseshoe Prior in Estimating High‐Dimensional Precision Matrix

ABSTRACTPrecision matrices are crucial in many fields such as social networks, neuroscience and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off‐diagonal position of the precision matrix indicates conditional independence between nodes. In high‐dimensional settings where the dimension of the precision matrix exceeds the sample size and the matrix is sparse, methods like graphical Lasso, graphical SCAD and CLIME are popular for estimating GGMs. While frequentist methods are well‐studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate, applying the global‐local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high‐dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior. A concise set of simulations is performed to validate our theoretical findings.

Bayesian Multilayered Mediation Analysis for Cancer Pharmacogenomics

ABSTRACTMultiomic data from multilevel biological systems are becoming common and motivate integrative modelling approaches to decipher within‐ and cross‐platform dependencies. Mediation analysis aims to identify mediating mechanisms that regulate the effect of an exposure on an outcome. In multiomic contexts, identification of genomic mediators of disease outcomes provides a deeper understanding of mechanisms of disease and corresponding therapeutic targets. While there has been significant work on joint modelling of high‐dimensional potential mediators, approaches that can identify individual mediators in presence of high‐dimensional potential mediators are lacking. We posit that the multiomic data are interrelated following multilayered Gaussian graphical models that include undirected and directed acyclic graphs as special cases. We develop a Bayesian inferential framework for multilayered mediation analysis with continuous, binary, and ordinal outcomes using probit models. As opposed to existing approaches focusing on identifying joint mediation effects, we decompose the joint effect into effects attributable to individual mediators in the framework of interventional mediation analysis. Simulations demonstrate our method outperforms other existing approaches to identify mediators that have nonzero indirect effects to the outcome. We apply our method to multiomic analysis on drug sensitivity outcomes of palbociclib and agents for endocrine therapy, standard care for breast cancer.

Interpersonal symptoms in adolescence depression across Asian and European regions: a network approach

BackgroundMajor Depressive Disorder (MDD) poses a significant global health challenge, with symptom presentation potentially varying between adolescents and adults. Adolescence is a critical period marked by heightened vulnerability to interpersonal stresses, yet the impact of these stresses on the structure of depressive symptoms is not well understood. Recognizing the cultural nuances in how depression manifests among adolescents is crucial. To this end, this paper employs a network analysis approach, utilizing a comprehensive symptom checklist from the Multidimensional Depression Assessment Scale (MDAS). Our study investigates the role of interpersonal symptoms within the broader cluster of emotional, cognitive, and somatic symptoms and explores variations in adolescent groups in four Asian and European regions.MethodsWe recruited a diverse sample of 6,348 adolescents aged 12 to 18 from Hong Kong, Taiwan, the UK, China, and the Netherlands using the Qualtrics platform. Employing the Gaussian Graphical Model, we established a network model of depressive symptoms as measured by the MDAS, segregating the sample into Asian and European regions to examine the interconnections between them. The study focused on identifying central symptom nodes and comparing the network structures between the two groups.ResultsThe analysis identified feeling worthless, low energy, being a burden to others, and low mood as central symptoms of depression. Notably, there were significant differences in the connections between depressive symptoms among Asian (Hong Kong, China and Taiwan) and European (UK and the Netherlands) adolescents, highlighting cultural variations in how interpersonal symptoms interact with emotional, cognitive, and somatic symptoms.ConclusionThis study is pioneering in applying network analysis to include interpersonal symptoms in examining depression among a diverse adolescent population. It demonstrates that interpersonal symptoms are integral to the central features of depressive symptoms. Furthermore, our findings suggest that, compared to their UK and Dutch peers, interpersonal symptoms in Asian adolescents are uniquely connected to other symptom clusters, reflecting distinct cultural patterns. Limitations: The study engaged a broad community sample; however, future research could benefit from including a larger sample size to allow for a more detailed analysis of a greater number of symptom nodes.

A new way to conceptualize intolerance of uncertainty among adolescents: Embracing the network perspective.

Intolerance of uncertainty (IU), a pivotal transdiagnostic risk factor in psychopathology, is defined as a dispositional incapacity to withstand uncertainty distress, driving maladaptive cognitive, emotional and behavioural reactions to uncertainty. However, the intricate interplay among these components, particularly in adolescents, remains underexplored; yet understanding this interplay is crucial for supporting mental health. To address this gap, we employed a network approach to conceptualize IU in 5672 non-clinical Chinese adolescents (Mage = 14.13 years, SDage = 1.96 years, range = 10-19 years, 46.6% boys), combining graphical Gaussian models (GGM) and directed acyclic graphs (DAG). Our analyses revealed a tripartite network comprising cognitive, behavioural and emotional components. Notably, 'frustration' and 'work with hindrance' emerged as key drivers, while 'catastrophizing belief' served as a critical bridge linking different components. These findings underscore the importance of alleviating uncertainty-induced frustration and enhancing coping skills for behavioural impediments to mitigate adolescent IU. Additionally, therapeutic interventions should prioritize modifying and re-evaluating catastrophizing beliefs related to uncertainty.

Using Network Analysis to Examine the Brain Regions Connectivity of Functional Neurological Disorder Patient and Healthy Participant

Introduction: Functional neurological disorder (FND) is one of the most common causes of neuropathy, However, its cause continues to be mysterious. Understanding the underlying mechanisms of that is crucial for treatment strategies. The study was conducted on brain images resting state fMRI taken from two volunteers (functional neurological disorder patient and healthy subject)who had the same characteristics. Methods: We fitted Gaussian Graphical Models to a single subject data using a network approach. Results: Based on the results of the networks, the number of significant edges was more in the left hemisphere in the patient, but in the healthy person, the number of these non-zero edges was more in the right hemisphere. Both the networks related to the healthy person and the patient had high density. Therefore, it indicated that the regions considered by these 2 people were strongly related to each other. The results showed the existence of more links and positive relationships between the regions, most of which showed a strong relationship. Among these connections, there were also negative connections. The networks of the healthy participant with almost symmetrical structures and the patient with Functional neurological disorder showed different characteristics, including asymmetry between the hemispheres. Conclusion: this study is the first to demonstrate that the brain regions of both functional neurological disorder patient and healthy participant can be conceptualized as networks. The findings of this study add to a growing body of literature that functional neurological disorder patient brain regions can be analyzed using network approaches.

Emotion Regulation, Eating Psychopathology, and Putative Transdiagnostic Psychological Processes: Findings from an Exploratory Network Analysis in a College Sample

Objective: Considering the prevalence of ED-related prodromal symptoms among higher education students (making them a population at risk for developing EDs), the main goals of this study were to conduct a network analysis in a college sample and to explore multivariate dependencies between a selection of empirically informed variables of interest to eating psychopathology, namely difficulties in emotion regulation and psychological processes (e.g., interoceptive awareness, self-compassion, self-criticism, mindfulness, and experiential avoidance). Methods: The sample included 294 college students (Mage = 21.4, SD = 5.0; MBMI = 22.4, SD = 3.7). A Gaussian graphical network model was estimated to visualize interactions among the studied variables and to assess their centrality in terms of betweenness, closeness, strength, and expected influence. Results: A network system with 21 nodes was estimated (sparsity = 0.52). Nodes assessing disordered eating symptoms displayed the strongest correlation coefficients with nodes assessing dimensions of interoceptive awareness: eating concerns and not-distracting (r = −0.11), shape concerns and trusting (r = −0.16), and weight concerns and trusting (r = −0.10). Self-compassion was the node with the highest betweenness (SELFCS = 2.27) and closeness centrality (SELFCS = 1.70). The nodes with the highest strength centrality were strategies (DERS = 1.91) and shape concerns (EDE-Q = 1.51). Discussion: In this network model conducted in a college sample, eating-related symptoms were mainly associated with dimensions of interoceptive awareness. Also, the lack of effective strategies to regulate emotions, shape concerns, and self-compassion stood out as central nodes in the network model. The results suggest that addressing these variables may be promising in disrupting network systems marked by the presence of prodromal eating psychopathology symptoms in at-risk populations (e.g., college students).

Efficient Distributed Transfer Learning for Large‐Scale Gaussian Graphic Models

ABSTRACTA transfer learning for the large‐scale Gaussian graphical models (GGMs) is considered in a distributed architecture for fitting these target and auxiliary studies scattered across multiple sites. A distributed transfer learning algorithm, DisPower‐Trans‐CLIME, is proposed to learn the target GGMs by incorporating the data from similar and related auxiliary studies. The algorithm is communication efficient via the distributed power method for matrix decomposition. We show that DisPower‐Trans‐CLIME has a fast convergence rate comparable to the centred Trans‐CLIME algorithm. A debiased DisPower‐Trans‐CLIME is constructed and is proved to be element‐wise asymptotically normal for statistical inference. Thus, a multiple testing procedure is developed to detect edge of GGMs with false discovery rate (FDR) control. Extensive simulation experiments have been conducted to demonstrate superior numerical performance of our proposed learning algorithm on estimation and edge detection. It is also applied to infer the regional connection networks in brain regions of interest (ROIs) based on a target hospital site by leveraging the graph from multiple other hospital sites for autism spectrum disorder. We observe that the degrees of regional connectivity in the right brain are balanced, while the ones of the left brain region are extremely uneven because of the presence of multiple strong connections. However, the specific association, between the degrees of connectivity of these regions and ASD disease, is unknown.

A network analysis of affective and motivational individual differences and error monitoring in a non-clinical sample.

Error monitoring, which plays a crucial role in shaping adaptive behavior, is influenced by a complex interplay of affective and motivational factors. Understanding these associations often proves challenging due to the intricate nature of these variables. With the aim of addressing previous inconsistencies and methodological gaps, in this study, we utilized network analysis to investigate the relationship between affective and motivational individual differences and error monitoring. We employed six Gaussian Graphical Models on a non-clinical population ($N$ = 236) to examine the conditional dependence between the amplitude of response-related potentials (error-related negativity; correct-related negativity) and 29 self-report measures related to anxiety, depression, obsessive thoughts, compulsive behavior, and motivation while adjusting for covariates: age, handedness, and latency of error-related negativity and correct-related negativity. We then validated our results on an independent sample of 107 participants. Our findings revealed unique associations between error-related negativity amplitudes and specific traits. Notably, more pronounced error-related negativity amplitudes were associated with increased rumination and obsessing, and decreased reward sensitivity. Importantly, in our non-clinical sample, error-related negativity was not directly associated with trait anxiety. These results underscore the nuanced effects of affective and motivational traits on error processing in healthy population.

Symptom Network Analysis and Unsupervised Clustering of Oncology Patients Identifies Drivers of Symptom Burden and Patient Subgroups With Distinct Symptom Patterns.

Interindividual variability in oncology patients' symptom experiences poses significant challenges in prioritizing symptoms for targeted intervention(s). In this study, computational approaches were used to unbiasedly characterize the heterogeneity of the symptom experience of oncology patients to elucidate symptom patterns and drivers of symptom burden. Severity ratings for 32 symptoms on the Memorial Symptom Assessment Scale from 3088 oncology patients were analyzed. Gaussian Graphical Model symptom networks were constructed for the entire cohort and patient subgroups identified through unsupervised clustering of symptom co-severity patterns. Network characteristics were analyzed and compared using permutation-based statistical tests. Differences in demographic and clinical characteristics between subgroups were assessed using multinomial logistic regression. Network analysis of the entire cohort revealed three symptom clusters: constitutional, gastrointestinal-epithelial, and psychological. Lack of energy was identified as central to the network which suggests that it plays a pivotal role in patients' overall symptom experience. Unsupervised clustering of patients based on shared symptom co-severity patterns identified six patient subgroups with distinct symptom patterns and demographic and clinical characteristics. The centrality of individual symptoms across the subgroup networks differed which suggests that different symptoms need to be prioritized for treatment within each subgroup. Age, treatment status, and performance status were the strongest determinants of subgroup membership. Computational approaches that combine unbiased stratification of patients and in-depth modeling of symptom relationships can capture the heterogeneity in patients' symptom experiences. When validated, the core symptoms for each of the subgroups and the associated clinical determinants may inform precision-based symptom management.

A Network Analytic Approach to Dissociation: New Insights from Clinical Data

ABSTRACT The transdiagnostic construct of dissociation, characterized by a disintegration of specific psychological functions such as consciousness, memory, identity, perception, body representation, and behavior, remains elusive to a unified conceptualization. Specifically, its dimensionality is a matter of ongoing controversy. Empirical approaches applying factor analyses to the Dissociative Experiences Scale (DES) have yielded inconsistent findings. This study adopts a novel methodological approach, utilizing Exploratory Graph Analysis (EGA) to address this issue. In a sample of 668 day-hospital patients undergoing psychotherapy for a variety of mental disorders, a Gaussian graphical model was estimated for the 28 items of the DES. Additionally, the stability of the results was ensured by bootstrap procedures. While both the original EGA and the bootstrap EGA suggested four dimensions, the structural consistency of this solution was low due to an instability of 12 items. After excluding 10 of these unstable items, re-analyses again revealed a four-factor structure, but boot EGA indicated that one factor had unsatisfactory structural consistency due to the multidimensionality of its two items. Upon removing these, our final network consisted of 16 items mapping onto 3 dimensions. Our study, using data from a diagnostically heterogeneous sample, replicates and extends previous findings on the dimensionality of dissociation as captured by the DES. The three dimensions identified correspond to segregated processes, derealization/depersonalization, and absorption. This solution aligns with a bipartite model of dissociation with two broader categories referring to either altered states of consciousness (often named detachment) or to non-integrated mental modules (labeled as compartmentalization).

Understanding internal dynamics of state anxiety during COVID‐19 pandemic: Seven‐wave longitudinal findings via panel network analysis

AbstractResearch on state anxiety has long been dominated by the traditional psychometric approach that assumes anxiety symptoms have a common cause. Yet state anxiety can be conceptualized as a network system. In this study, we utilized data from the COVID‐Dynamic dataset from waves 7 to 13, collected at three‐week intervals from June 6, 2020, to October 13, 2020, and included 1,042 valid participants to characterize the internal dynamics of state anxiety. Using the Gaussian graphical model along with strength centrality, we estimated three network models of state anxiety. The between‐subjects and contemporaneous network showed numerous positive relations between items and some unexpected negative relations. Three communities were identified in the between‐subjects network, and two communities were identified in the contemporaneous network. The temporal network showed the coexistence of positive and negative predictions between items after three weeks. Several items exhibited significant positive autocorrelations after three weeks. These findings have implications for anxiety theory and clinical interventions at between‐subjects and within‐subjects levels.

Depressive symptoms, cognitive functions and daily activities: An extended network analysis in monozygotic and dizygotic twins

BackgroundThe network theory posits that depression emerges as the result of individual symptoms triggering each other. Risk factors for depression can impact these between-symptoms interactions through extended networks. The study aimed to model the extended network of depressive symptoms and known depression risk factors – objective cognitive function, intellectual, physical, and social daily activities, and then, compare the observed networks between monozygotic (MZ) and dizygotic (DZ) co-twins. MethodsTwin pairs, 722 MZ and 2200 DZ, aged 40–79, were selected from the Dansh Twin Registry for having complete measures of depressive symptoms (e.g., sadness), cognitive functions (e.g., verbal memory), physical (e.g., brisk walk), intellectual (e.g., reading newspapers) and social activities (e.g., phone calls). Gaussian graphical models were used to estimate and compare the networks first between co-twins and then, between MZ to DZ twin pairs separately. ResultsSpecific intellectual, physical and social activities were central in the extended networks of depressive symptoms and, with the exception of processing speed, more central than cognition. The extended networks' structure was more homogeneous between MZ co-twins relative to DZ co-twins. Cognitive nodes were more central in MZ than DZ co-twins. LimitationsCross-sectional design, participants were middle-aged or older, mostly affective (non-somatic) depressive symptoms. ConclusionsIn depression networks, core connecting elements were intellectual, physical and social activities. The interaction between cognition and daily activities seems critical for triggering depressive symptoms. Thus, clinical interventions aimed at preventing depression and associated cognitive deficits should focus on maintenance and/or engagement in stimulating daily activities.

Understanding the relationship between childhood abuse and affective symptoms in bipolar disorder: New insights from a network analysis

The impact of childhood abuse on the presentation of bipolar disorder could be further elucidated by comparing the networks of affective symptoms among individuals with and with no history of childhood abuse. Data from 476 participants in the Clinical Health Outcomes Initiative in Comparative Effectiveness for Bipolar Disorder study were used to fit several regularised Gaussian Graphical Models. Differences in the presentation of depressive and manic symptoms were uncovered: only among participants with a history of childhood abuse, inadequacy and pessimism were central symptoms in the network of depressive symptoms, while racing thoughts was an important symptom in the network of manic symptoms. Following network theory, focusing treatments at the symptom-level and on central symptoms – like inadequacy, pessimism, and racing thoughts – could be an effective approach for managing affective symptoms among the sizeable proportion of people with bipolar disorder who have experienced childhood abuse. This study contributes a thorough investigation of the networks of affective symptoms among participants with and with no history of childhood abuse, albeit limited by the use of a binary, self-report measure of childhood abuse, thereby emphasising the importance of assessing for childhood abuse and taking needed steps towards identifying novel targets for treating bipolar disorder.

Unpacking interplays between competitiveness, cooperativeness, and social comparison orientation: A network psychometric approach and replication.

Emerging evidence highlights the role of social comparison in competition and cooperation, yet the dynamics among competitiveness, cooperativeness, and social comparison orientation (SCO) remain underexplored. In the present study, we sought to unravel these complex interplays employing graphical Gaussian models (GGMs) and characterize the network structures utilizing cross-sectional data derived from 1073 Chinese participants. A pre-registered independent sample (n = 1348) served to examine the replicability and robustness of our initial findings. Moreover, we explored the Bayesian networks (i.e., directed acyclic graphs) to delve into their probabilistic directed dependencies. Our analysis identified an interpersonal co-opetition network where SCO bridges competitiveness and cooperativeness, emphasizing the key influence of the desire to surpass others. We also found a significant gender effect on the levels of these orientations but not on the network patterns. Additionally, the replication sample offered validation for the resultant network structure and its key nodes. In sum, these findings provide a new insight into the symbiotic relationship between competitiveness and cooperativeness within the framework of social comparison, offering significant theoretical and practical implications.

The Common Structure of the Major Psychoses: More Similarities Than Differences in the Network Structures of Schizophrenia, Schizoaffective Disorder, and Psychotic Bipolar Disorder.

There has been a century-long debate about whether the major psychoses (eg, bipolar disorder, schizophrenia, and schizoaffective disorder) are one disorder with various manifestations or different disease entities. Traditional approaches using dimensional models have not provided decisive findings. Here, we address this question by examining the network constellation of affective and psychotic syndromes. Comparable symptom data of 1882 patients with psychotic bipolar disorder, schizoaffective disorders, and schizophrenia were extracted from three datasets: B-SNIP 1, B-SNIP2, and PARDIP. Twenty-six items from the Positive and Negative Syndrome Scale, YMRS, and the Montgomery-Asberg Depression Rating Scale were selected for the analysis using a principled approach to eliminate overlapping/redundant items. Gaussian graphical models were estimated and assessed for stability, and their communities were identified using bootstrapped exploratory graph analysis. The structures and global densities of the networks were compared with network comparison tests. The network structures were highly similar (r >. 80) across diagnostic groups. For all diagnoses, manic symptoms were more connected with positive symptoms while depressive symptoms were more linked with negative symptoms. The depressive and negative symptoms were the strongest indicators of depressive and psychotic communities. Theoretically interesting variability in network edge weights between symptoms was found relating to thought disorder and pessimistic thinking. The same broad structure of psychopathology underlies the symptom expressions of bipolar disorder, schizoaffective disorder, and schizophrenia. Future studies should build on the present finding by comparing specific inter-relations between symptoms in the different diagnostic groups using methods capable of detecting causality.

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.