Graphical Lasso Algorithm Research Articles

Identifying stationary microbial interaction networks based on irregularly spaced longitudinal 16S rRNA gene sequencing data

IntroductionThe microbial interactions within the human microbiome are complex, and few methods are available to identify these interactions within a longitudinal microbial abundance framework. Existing methods typically impose restrictive constraints, such as requiring long sequences and equal spacing, on the data format which in many cases are violated.MethodsTo identify microbial interaction networks (MINs) with general longitudinal data settings, we propose a stationary Gaussian graphical model (SGGM) based on 16S rRNA gene sequencing data. In the SGGM, data can be arbitrarily spaced, and there are no restrictions on the length of data sequences from a single subject. Based on the SGGM, EM -type algorithms are devised to compute the L1-penalized maximum likelihood estimate of MINs. The algorithms employ the classical graphical LASSO algorithm as the building block and can be implemented efficiently. ResultsExtensive simulation studies show that the proposed algorithms can significantly outperform the conventional algorithms if the correlations among the longitudinal data are reasonably high. When the assumptions in the SGGM areviolated, e.g., zero inflation or data from heterogeneous microbial communities, the proposed algorithms still demonstrate robustness and perform better than the other existing algorithms. The algorithms are applied to a 16S rRNA gene sequencing data set from patients with cystic fibrosis. The results demonstrate strong evidence of an association between the MINs and the phylogenetic tree, indicating that the genetically related taxa tend to have more/stronger interactions. These results strengthen the existing findings in literature. DiscussionThe proposed algorithms can potentially be used to explore the network structure in genome, metabolome etc. as well.

A network analysis of early trauma and impulsive behavior in individuals with alcohol, cocaine, and polysubstance use disorder.

This study investigated the relationship between impulsivity and early trauma through a network analysis in individuals diagnosed with different substance use disorders. In a cross-sectional design, the sample included 556 men with substance use disorders (195 with alcohol use, 157 with cocaine/crack use, and 214 with polysubstance use). Early trauma and impulsive behavior were assessed using the Childhood Trauma Questionnaire and the Barratt Impulsiveness Scale, respectively. The connection between trauma and impulsivity was assessed using network analysis through a fused graphical lasso algorithm. No connection was observed between impulsivity and trauma networks in individuals with alcohol use disorder. In those with cocaine use disorder, networks were linked through the motor domain and sexual abuse nodes. Inverse connections were observed between the emotional neglect node and perseverance, but not the non-planning node. In polysubstance use, the connection between impulsivity and trauma networks was weak, with the cognitive complexity node connecting to the trauma network through physical abuse. There connections were inversely proportional between the motor domain and emotional neglect nodes, as well as between cognitive instability and physical neglect. Our results suggest that the relationship between the type of early (childhood) trauma and the expression of impulsivity could lead to different substance use profiles.

Inferring Diagnostic and Prognostic Gene Expression Signatures Across WHO Glioma Classifications: A Network-Based Approach.

Tumor heterogeneity is a challenge to designing effective and targeted therapies. Glioma-type identification depends on specific molecular and histological features, which are defined by the official World Health Organization (WHO) classification of the central nervous system (CNS). These guidelines are constantly updated to support the diagnosis process, which affects all the successive clinical decisions. In this context, the search for new potential diagnostic and prognostic targets, characteristic of each glioma type, is crucial to support the development of novel therapies. Based on The Cancer Genome Atlas (TCGA) glioma RNA-sequencing data set updated according to the 2016 and 2021 WHO guidelines, we proposed a 2-step variable selection approach for biomarker discovery. Our framework encompasses the graphical lasso algorithm to estimate sparse networks of genes carrying diagnostic information. These networks are then used as input for regularized Cox survival regression model, allowing the identification of a smaller subset of genes with prognostic value. In each step, the results derived from the 2016 and 2021 classes were discussed and compared. For both WHO glioma classifications, our analysis identifies potential biomarkers, characteristic of each glioma type. Yet, better results were obtained for the WHO CNS classification in 2021, thereby supporting recent efforts to include molecular data on glioma classification.

Graphiclasso: Graphical lasso for learning sparse inverse-covariance matrices

In modern multivariate statistics, where high-dimensional datasets are ubiquitous, learning large (inverse-) covariance matrices is imperative for data analysis. A popular approach to estimating a large inverse-covariance matrix is to regularize the Gaussian log-likelihood function by imposing a convex penalty function. In a seminal article, Friedman, Hastie, and Tibshirani (2008, Biostatistics 9: 432–441) proposed a graphical lasso (Glasso) algorithm to efficiently estimate sparse inverse-covariance matrices from the convex regularized log-likelihood function. In this article, I first explore the Glasso algorithm and then introduce a new graphiclasso command for the large inverse-covariance matrix estimation. Moreover, I provide a useful command for tuning parameter selection in the Glasso algorithm using the extended Bayesian information criterion, the Akaike information criterion, and cross-validation. I demonstrate the use of Glasso using simulation results and real-world data analysis.

GRAFİKSEL LASSO İLE PORTFÖY OPTİMİZASYONU VE BORSA İSTANBUL’DA BİR UYGULAMA

Graphical Lasso (Least absolute shrinkage and selection operator) has become a popular tool in the field of machine learning in recent years. Although it has been deployed mainly for feature selection in classification problems, it is also used for covariance matrix estimation. Mean-variance portfolio optimization relies on sample covariance matrix for the calculation of the portfolio’s risk, whereas it has been most hardly criticized. The aim of this study is to demonstrate the effect of the covariance matrix estimation by Graphical Lasso algorithm with varying L1 penalty factors. Mean-variance portfolio optimization using empirical and estimated covariance matrices are applied to BIST 30 index and the results are compared.

The architecture of psychological well-being: A network analysis study of the Ryff Psychological Well-Being Scale.

The proliferation of mental health research is orienting its efforts towards the exploration of psychological well-being. One of the main burdens is the measurement challenges reported by the widely used Psychological Well-Being Scale (PWBS), which has often been criticized for inconsistencies between the theoretical and the empirical model. A potential alternative to understand the structure of psychological well-being is network models, which conceptualizes psychological phenomena as emerging systems of mutually connected variables. Employing exploratory graph analysis, we examined the network structure of the Spanish 29-item PWBS in a random sample of 1,404 adults. We estimated a regularized partial correlation network using the graphical LASSO algorithm in the item and dimension level. We tested the stability of both networks and identified the most important variables of the network. The PWBS network model revealed four dimensions, with self-acceptance, life purpose and environmental mastery clustering together. Node strength centrality suggested that self-acceptance is the most central dimension in the psychological well-being structure as measured by the PWBS. Despite the network model of psychological well-being did not replicate the theoretical structure of Ryff's model, it provides a novel conceptualization of psychological well-being and proposes target indicators for mental health interventions.

Selection of Multiple Donor Gauges via Graphical Lasso for Estimation of Daily Streamflow Time Series

AbstractA fundamental challenge in estimations of daily streamflow time series at sites with incomplete records is how to effectively and efficiently select reference/donor gauges from an existing gauge network to infer the missing data. While research on estimating missing streamflow time series is not new, the existing approaches either use a single reference streamflow gauge or employ a set of “ad hoc” reference gauges, leaving a systematic selection of reference gauges as a long‐standing open question. In this work, a novel method is introduced that facilitates a systematic selection of multiple reference gauges from any given streamflow network. The idea is to mathematically characterize the network‐wise correlation structure of a streamflow network via graphical Markov modeling and to further transform a dense network into a sparsely connected one. The resulted underlying sparse graph from the graphical model encodes conditional independence conditions among all reference gauges from the streamflow network, allowing determination of an optimum subset of the donor gauges. The sparsity is discovered by using the Graphical Lasso algorithm with an L1 norm regularization parameter and a thresholding parameter. These two parameters are determined by a multi‐objective optimization process. Furthermore, the graphical modeling approach is employed to solve another open problem in gauge removal planning decision (e.g., due to operation budget constraints): which gauges to remove would statistically guarantee the least loss of information by estimations from the remaining gauges? Our graphical model‐based method is demonstrated with daily streamflow data from a network of 34 gauges over the Ohio River basin region.

Estimation of Undirected Graph with Finite Mixture of Nonparanormal Distribution

In this paper, the nonparanormal graphical mixture model is introduced as a flexible multivariate analysis tool with a semiparametric approach. In this model, mixture component densities are nonparanormal distributions with different covariance matrices. Therefore, each mixture component may have a different dependency structure with the probability of the respective mixture proportion. Our suggested estimation algorithm uses expectation maximization algorithm for maximization of $$\ell _1$$ -regularized likelihood function. Graphical lasso algorithm and extended Bayesian information criterion are used in each iteration of the EM algorithm for the model selection purposes. Simulation studies show that the proposed method performs better than the alternative Gaussian graphical mixture model, especially for non-Gaussian heterogeneous data. The proposed method is also applied to water-level dataset and is compared with the results of Gaussian mixture model.

Network Analysis of Competitive State Anxiety.

Competitive state anxiety is an integral feature of sports performance but despite its pervasiveness, there is still much debate concerning the measurement of the construct. Adopting a network approach that conceptualizes symptoms of a construct as paired associations, we proposed re-examining competitive state anxiety as a system of interacting components in a dataset of 485 competitive athletes from the United Kingdom. Following a process of data reduction, we estimated a network structure for 15 items from the modified Three Factor Anxiety Inventory using the graphical LASSO algorithm. We then examined network connectivity using node predictability. Exploratory graph analysis was used to detect communities in the network and bridge expected influence calculated to estimate the influence of items from one community to items in other communities. The resultant network produced a range of node predictability values. Community detection analysis derived three communities that corresponded with previous research and several nodes were identified that bridged these communities. We conclude that network analysis is a useful tool to explore the competitive state anxiety response and we discuss how the results of our analysis might inform the assessment of the construct and how this assessment might inform interventions.

Estimating high-dimensional covariance and precision matrices under general missing dependence

A sample covariance matrix S of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis, and testing of equality of mean vectors. However, when the data are partially observed, the sample covariance matrix from the available data is biased and does not provide valid multivariate procedures. To correct the bias, a simple adjustment method called inverse probability weighting (IPW) has been used in previous research, yielding the IPW estimator. The estimator can play the role of S in the missing data context, thus replacing S in off-the-shelf multivariate procedures such as the graphical lasso algorithm. However, theoretical properties (e.g. concentration) of the IPW estimator have been only established in earlier work under very simple missing structures; every variable of each sample is independently subject to missingness with equal probability. We investigate the deviation of the IPW estimator when observations are partially observed under general missing dependency. We prove the optimal convergence rate Op( logp∕n) of the IPW estimator based on the element-wise maximum norm, even when two unrealistic assumptions (known mean and/or missing probabilities) frequently assumed to be known in the past work are relaxed. The optimal rate is especially crucial in estimating a precision matrix, because of the “meta-theorem” [26] that claims the rate of the IPW estimator governs that of the resulting precision matrix estimator. In the simulation study, we discuss one of practically important issues, non-positive semi-definiteness of the IPW estimator, and compare the estimator with imputation methods.

An integrated framework for visualizing and forecasting realized covariance matrices

This paper proposes an integrated framework for visualizing and forecasting realized covariance matrices to enable the efficient construction and prediction of an optimal portfolio. Multivariate realized kernels are typically derived from intra-day high-frequency data, and are then used to estimate the realized covariance matrix via the graphical lasso algorithm. To forecast the realized covariances, we employ the conditional autoregressive Wishart model and its variants. Finally, we compute the Stein loss function and execute the model-confidence-set procedure to obtain the best model for optimal portfolio selection.

An Integrated Framework for Visualizing and Forecasting Realized Covariance Matrices

This paper proposes an integrated framework for visualizing and forecasting realized covariance matrices to enable efficient construction and prediction of an optimal portfolio. Multivariate realized kernels are typically derived from intra-day high-frequency data, and the realized covariance matrix is estimated from the kernels using the graphical LASSO algorithm. To forecast the realized covariances, we employ the conditional autoregressive Wishart (CAW) model and its variants. Finally, we compute the Stein loss function and execute the model-confidence-set (MCS) procedure to obtain the best model for optimal portfolio selection.

Estimating sparse networks with hubs

Graphical modelling techniques based on sparse estimation have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance and social sciences. One structural feature of some of these networks that poses a challenge for statistical inference is the presence of a small number of strongly interconnected nodes, which are called hubs. For example, in microbiome research hubs or microbial taxa play a significant role in maintaining stability of the microbial community structure. In this paper, we investigate the problem of estimating sparse networks in which there are a few highly connected hub nodes. Methods based on L1-regularization have been widely used for performing sparse estimation in the graphical modelling context. However, while these methods encourage sparsity, they do not take into account structural information of the network. We introduce a new method for estimating networks with hubs that exploits the ability of (inverse) covariance estimation methods to include structural information about the underlying network. Our method is a weighted lasso approach with novel row/column sum weights, which we refer to as the hubs weighted graphical lasso. A practical advantage of the new method is that it leads to an optimization problem that is solved using the efficient graphical lasso algorithm that is already implemented in the R package glasso (Friedman et al., 2019). We establish large sample properties of the method when the number of parameters diverges with the sample size. We then show via simulations that the method outperforms competing methods and illustrate its performance with an application to microbiome data.

Examining a Syndemics Network Among Young Latino Men Who Have Sex with Men.

Although studies consistently find that syndemic indicators are additively associated with increased HIV/STI risk behavior (e.g., condomless anal sex; CAS) among men who have sex with men (MSM), information is lacking about how syndemic indicators are associated with each other. Young Latino MSM are one of the most at-risk groups for acquiring HIV in the U.S. Understanding the associations of syndemic indicators with each other and with CAS may improve understanding of how to enhance sexual and behavioral health in this population. Network analysis using the graphical LASSO (glasso) algorithm was employed to explore associations between CAS and syndemic indicators among 139 young Latino MSM. Structural and psychosocial syndemic indicators were assessed via self-report. CAS was defined as the number of partners in the past 3months with whom one engaged in CAS. Results of the network analysis suggested the variables with the highest centrality were unstable housing, prison history, childhood sexual abuse, and CAS. Specific significant associations included links between CAS and alcohol use (b = 0.40), childhood sexual abuse and unstable housing (b = - 0.75), alcohol use and childhood sexual abuse (b = 0.40), and substance use and intimate partner violence (b = 0.43). This pattern of interconnectedness demonstrates the potential for network analysis to examine nuanced interrelationships of syndemic indicators. The specific associations in this sample raise the question whether a primary focus of interventions should address the more central syndemic indicators for this population, such as alcohol use and unstable housing, and whether this would, via downstream effects, affect other aspects of behavioral health in this population.

Abstract 3820: Discovery of adaptive resistance pathways and anti-resistance combination therapies from phosphoproteomic data using graphical models

Abstract Introduction. Resistance to targeted therapies, either intrinsic (pre-existing at the time of treatment) or acquired (emerges as the tumor adapts to therapy), is a major challenge in oncology. Blocking multiple escape routes using drug combinations is the best solution to drug resistance. However, the discovery of effective combinations remains a challenging task due to complexity of the underlying biological processes and inter-tumor heterogeneity. Here, we developed a statistical pathway analysis method that (i) reveals pathways involved in drug activity and adaptive resistance and (ii) nominates combination therapies to down-regulate the resistance pathways. The method is based on the rationale that (i) targeting a specific genomic aberration may lead to activation of compensatory pathways (e.g. via feedback loops in the short term) and subsequent resistance, and (ii) collective changes in pathway activities are better predictors of resistance and mitigation strategies than abundances of individual molecules. Method. We construct a network model of signaling interactions using an adjusted graphical LASSO (GLASSO) algorithm from RPPA data. This is supplemented with prior pathway information from multiple signaling databases (using Pathway Commons) to estimate sparse directed graphical models. Next, we combine the network with the cell- type-specific drug response data to calculate a target score (TS) for each protein. The TS quantifies the adaptive pathway responses to a perturbation by integrating the change in the level of a (phospho)protein and its pathway neighborhood in response to a perturbation. A high TS corresponds to involvement in adaptive response (e.g. RTK upregulation by MEK inhibitor via a feedback loop) and a low TS corresponds to the activity of the drug (e.g. ERK phosphorylation inhibition by MEK inhibitor). Finally, by identifying the subnetworks with enriched, high TS values, we determine the adaptive resistance pathways. We validate the resulting predictions (combinations of the original drug perturbation with drugs targeting the resistance pathways) experimentally. Applications. The method is amenable to calculations for hundreds of samples treated with individual (or combinations of) drugs in multiple doses and/or time points and interrogated for thousands of molecular entities (mRNA or proteomic). With longitudinal data, we will be able to explain the evolution of drug resistance and potentially the optimum time points for intervention. The protocol is defined with a focus on RPPA data, but can be adapted to other kinds of molecular data associated with adaptive responses. We applied our method to BET-BRD inhibition in ovarian and breast cancers to compare resistance/response pathways in cells with varying sensitivity. The analysis nominated cell-type-specific anti-resistance combinations involving BET inhibitors. Citation Format: Augustin Luna, Heping Wang, Ozgun Babur, Chris Sander, Anil Korkut. Discovery of adaptive resistance pathways and anti-resistance combination therapies from phosphoproteomic data using graphical models [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 3820.

Microbial assessments of soil with a 40-year history of reclaimed wastewater irrigation

The long-term effects on soil microorganisms from 40 years of irrigating soil with reclaimed wastewater was investigated by determining the quantity, composition, and inter-species connection of microorganisms. No significant difference in microbial quantity and composition were identified in the reclaimed wastewater- and groundwater-irrigated soils. The dominant bacterial phylum in both irrigation water sources and soils was Proteobacteria, which commonly exists in soil. From the analysis of four (4) alpha diversity metrics, including the observed number of operational taxonomic units (OTUs), Chao1, and the Shannon and Simpson diversity, there was no significant difference between the reclaimed wastewater- and groundwater-irrigated soils. Three zones (shallow, medium and deep) were identified in the reclaimed wastewater- and groundwater-irrigated soils based on the taxonomic networks and clusters generated by graphical lasso and random walk algorithm. The cluster profiles (shallow, medium and deep zones) appear to be different in the reclaimed wastewater- and groundwater-irrigated soils. Soil irrigated with reclaimed wastewater showed less depth of clustered profile in medium zone than that in soil irrigated with groundwater (20–60 cm of reclaimed wastewater-irrigated soil compared to 20–100 cm of groundwater-irrigated soil), although the significance of such a variance (the depth of medium zone of reclaimed wastewater-irrigated soil decreased 40 cm than that of groundwater-irrigated soil) is not clear at this time. Positive influence has been identified in the growth and yield of eggplant, tomato and cucumber between the reclaimed wastewater- and groundwater-irrigated soils, suggesting that reclaimed wastewater irrigation can potentially substitute groundwater irrigation, despite the variance in inter-species clustering profiles in soil microbes in certain soil zones. Nevertheless, the possible negative influence of pathogens, organic compounds and pharmaceuticals should be seriously considered during the reclaimed wastewater irrigation.

Modeling inter-country spatial financial interactions with Graphical Lasso: An application to sovereign co-risk evaluation

We propose a model to extract significant risk spatial interactions between countries adopting the Graphical Lasso algorithm, used in graph theory to sort out spurious conditional correlations. In this context, the major issue is the definition of the penalization parameter. We propose a search algorithm aimed at the best separation of the variables (expressed in terms of conditional dependence) given an a priori desired partition. The case study focuses on Credit Default Swap (CDS) returns over the period 2009–2017. The proposed algorithm is used to estimate the spatial systemic risk relationship between Peripheral and Core Countries in the Euro Area.

Mapping network connectivity among symptoms of social anxiety and comorbid depression in people with social anxiety disorder

BackgroundSocial anxiety disorder (SAD) and depressive symptoms often covary. Yet, uncertainty still abounds vis-à-vis the individual symptom-to-symptom associations between these two disorders. Inspired by the network approach to psychopathology that conceptualizes comorbidity as a natural consequence arising from bridge symptoms that can transmit activation from one disorder to the other, we applied network analytic methods to characterize the associations among core symptoms of SAD—i.e. fear and avoidance of social situations—and comorbid depressive symptoms among 174 individuals with DSM-IV-TR criteria for SAD. MethodsWe first explored the general structure of these symptoms by estimating a regularized partial correlation network using the graphical LASSO algorithm. Then, we specifically focused on the symptoms’ importance and influence. Of critical interest was the estimation of the unique influence of each symptom from one disorder to all symptoms of the other disorder using a new metric called bridge expected influence. ResultsThe graphical LASSO revealed several cross-associations between SAD and comorbid depression. For each disorder, symptoms exhibiting the strongest cross-association with the other disorder were identified. LimitationsGiven our cross-sectional data, our findings can only suggest hypotheses about cause-effect relationships. ConclusionsThis study adds to a small but growing empirical literature revealing that the co-occurrence between two disorders is best portrayed as sets of symptom-to-symptom connections. As some individual symptoms show differential association in the co-occurrence between SAD and depression, those symptoms may be valuable targets for future research and treatment.

Unsupervised Network Analysis of the Plastic Supraoptic Nucleus Transcriptome Predicts Caprin2 Regulatory Interactions.

The supraoptic nucleus (SON) is a group of neurons in the hypothalamus responsible for the synthesis and secretion of the peptide hormones vasopressin and oxytocin. Following physiological cues, such as dehydration, salt-loading and lactation, the SON undergoes a function related plasticity that we have previously described in the rat at the transcriptome level. Using the unsupervised graphical lasso (Glasso) algorithm, we reconstructed a putative network from 500 plastic SON genes in which genes are the nodes and the edges are the inferred interactions. The most active nodal gene identified within the network was Caprin2. Caprin2 encodes an RNA-binding protein that we have previously shown to be vital for the functioning of osmoregulatory neuroendocrine neurons in the SON of the rat hypothalamus. To test the validity of the Glasso network, we either overexpressed or knocked down Caprin2 transcripts in differentiated rat pheochromocytoma PC12 cells and showed that these manipulations had significant opposite effects on the levels of putative target mRNAs. These studies suggest that the predicative power of the Glasso algorithm within an in vivo system is accurate, and identifies biological targets that may be important to the functional plasticity of the SON.

Block-Diagonal Covariance Selection for High-Dimensional Gaussian Graphical Models

ABSTRACTGaussian graphical models are widely used to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a nonasymptotic model selection procedure supported by strong theoretical guarantees based on an oracle type inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network. Supplementary materials for this article are available online.