Sparse Inverse Covariance Estimation Research Articles

Network analysis of gut microbial communities reveal key genera for a multiple sclerosis cohort with Mycobacterium avium subspecies paratuberculosis infection

BackgroundIn gut ecosystems, there is a complex interplay of biotic and abiotic interactions that decide the overall fitness of an individual. Divulging the microbe-microbe and microbe-host interactions may lead to better strategies in disease management, as microbes rarely act in isolation. Network inference for microbial communities is often a challenging task limited by both analytical assumptions as well as experimental approaches. Even after the network topologies are obtained, identification of important nodes within the context of underlying disease aetiology remains a convoluted task. We therefore present a network perspective on complex interactions in gut microbial profiles of individuals who have multiple sclerosis with and without Mycobacterium avium subspecies paratuberculosis (MAP) infection. Our exposé is guided by recent advancements in network-wide statistical measures that identify the keystone nodes. We have utilised several centrality measures, including a recently published metric, Integrated View of Influence (IVI), that is robust against biases.ResultsThe ecological networks were generated on microbial abundance data (n = 69 samples) utilising 16 S rRNA amplification. Using SPIEC-EASI, a sparse inverse covariance estimation approach, we have obtained networks separately for MAP positive (+), MAP negative (-) and healthy controls (as a baseline). Using IVI metric, we identified top 20 keystone nodes and regressed them against covariates of interest using a generalised linear latent variable model. Our analyses suggest Eisenbergiella to be of pivotal importance in MS irrespective of MAP infection. For MAP + cohort, Pyarmidobacter, and Peptoclostridium were predominately the most influential genera, also hinting at an infection model similar to those observed in Inflammatory Bowel Diseases (IBDs). In MAP- cohort, on the other hand, Coprostanoligenes group was the most influential genera that reduces cholesterol and supports the intestinal barrier.ConclusionsThe identification of keystone nodes, their co-occurrences, and associations with the exposome (meta data) advances our understanding of biological interactions through which MAP infection shapes the microbiome in MS individuals, suggesting the link to the inflammatory process of IBDs. The associations presented in this study may lead to development of improved diagnostics and effective vaccines for the management of the disease.

Network analysis of gut microbial communities reveal key genera for a multiple sclerosis cohort with Mycobacterium avium subspecies paratuberculosis infection

BackgroundIn gut ecosystems, there is a complex interplay of biotic and abiotic interactions that decide the overall fitness of an individual. Divulging the microbe-microbe and microbe-host interactions may lead to better strategies in disease management, as microbes rarely act in isolation. Network inference for microbial communities is often a challenging task limited by both analytical assumptions as well as experimental approaches. Even after the network topologies are obtained, identification of important nodes within the context of underlying disease aetiology remains a convoluted task. We therefore present a network perspective on complex interactions in gut microbial profiles of individuals who have multiple sclerosis with and without Mycobacterium avium subspecies paratuberculosis (MAP) infection. Our exposé is guided by recent advancements in network-wide statistical measures that identify the keystone nodes. We have utilised several centrality measures, including a recently published metric, Integrated View of Influence (IVI), that is robust against biases.ResultsThe ecological networks were generated on microbial abundance data (n = 69 samples) utilising 16 S rRNA amplification. Using SPIEC-EASI, a sparse inverse covariance estimation approach, we have obtained networks separately for MAP positive (+), MAP negative (-) and healthy controls (as a baseline). Using IVI metric, we identified top 20 keystone nodes and regressed them against covariates of interest using a generalised linear latent variable model. Our analyses suggest Eisenbergiella to be of pivotal importance in MS irrespective of MAP infection. For MAP + cohort, Pyarmidobacter, and Peptoclostridium were predominately the most influential genera, also hinting at an infection model similar to those observed in Inflammatory Bowel Diseases (IBDs). In MAP- cohort, on the other hand, Coprostanoligenes group was the most influential genera that reduces cholesterol and supports the intestinal barrier.ConclusionsThe identification of keystone nodes, their co-occurrences, and associations with the exposome (meta data) advances our understanding of biological interactions through which MAP infection shapes the microbiome in MS individuals, suggesting the link to the inflammatory process of IBDs. The associations presented in this study may lead to development of improved diagnostics and effective vaccines for the management of the disease.

Reconfigured metabolism brain network in asymptomatic microtubule‐associated protein tau mutation carriers: A graph‐theoretical analysis

AbstractBackgroundStudies exploring topologic properties of the metabolic network in the presymptomatic stage of genetic frontotemporal dementia (FTD) are scarce, which may be important for understanding brain function and disease pathogenesis. This study aimed to explore FTD‐specific patterns of metabolism topology reconfiguration in asymptomatic microtubule‐associated protein tau (MAPT) mutation carriers.MethodSix asymptomatic carriers of MAPT P301L mutation were compared with 12 non‐carriers who were all from the same large family of FTD. For comparison, we included 32 behavioral‐variant FTD (bvFTD) patients and 33 unrelated healthy controls. Each participant underwent neuropsychological assessments, genetic testing, and hybrid PET/MRI scan. Voxel‐wise gray matter volume and standardized uptake value ratio were calculated and compared for structural MRI and FDG‐PET, separately. The sparse inverse covariance estimation (SICE) method was applied to topologic properties and metabolic connectomes of brain functional networks derived from 18F‐fluorodeoxyglucose PET/MRI data. Independent component analysis was used to explore metabolic connectivity in the salience (SN) and default mode networks (DMN).ResultThe mean estimated years from symptom onset was 8.33 ± 1.875 years in the mutation carrier group. The asymptomatic MAPT carriers show no significant differences in cognitive tests, gray matter volume and FDG uptake compared to non‐carriers. They also retained normal global parameters of metabolism network, but not for bvFTD patients. However, we revealed lost hubs in the ventromedial prefrontal, orbitofrontal, and anterior cingulate cortices and reconfigured hubs in the anterior insula, precuneus, and posterior cingulate cortex in asymptomatic carriers, which is consistent with the findings in bvFTD patients. Similarly, significant differences in local parameters of these nodes were observed in asymptomatic carriers. The reduction in connectivity was marked in lost hub regions during the asymptomatic stage. Functional connectivity within the SN and DMN was enhanced in asymptomatic carriers, while reduced in bvFTD patients.ConclusionOur findings showed that asymptomatic MAPT carriers were initially involved in medial prefrontal areas and actively compensated in task‐related regions. Topologic properties of the metabolic network may contribute to further investigations and monitoring of the earliest stages of FTD in individuals with genetic backgrounds.

Abstract 2364: Gut microbiome interacts with clinical characteristics on all-cause mortality of colorectal cancer patients

Abstract Background: Gut microbiota has been introduced to involve in the migration and invasion stage of metastasis of colorectal cancer (CRC) cells and interact with both the pharmacokinetics and pharmacodynamics of chemotherapeutic agents and immune checkpoint inhibitors. In this study, we examined microbiome features in association with all-cause mortality of CRC patients and examined their interactions with clinical factors. Methods: We performed 16S rRNA sequencing for 331 preoperative fecal samples of CRC patients at Seoul National University Hospital, Korea. Multiple Cox proportional hazard model was applied to calculate hazard ratios (HRs) and 95% confidence intervals (CIs) for the risk of all-cause mortality due to microbiome features (within-sample diversity indices, species patterns, genus abundance, and taxonomic co-occurrence networks) and clinical factors (tumor grade and stage, surgical methods, neoadjuvant and adjuvant therapies, and invasion). We added the multiplicative term into the model to test the interaction between gut microbiota and clinical characteristics. Results: During a median follow-up of 3.7 years, deaths from any causes were reported in 46 patients. From 172 species, the principal component analysis identified 4 patterns, which explained a total 66.1% variation in species abundance. Of 77 genera, 9 co-occurrence networks were identified by the SParse InversE Covariance Estimation for Ecological Association Inference. For genus level, the risk of death was positively associated with Butyricicoccus (HR=1.54, 95% CI=1.17-2.04), but inversely associated with Lactococcus (HR=0.60, 95% CI=0.37-0.95), Acidaminococcus (HR=0.57, 95% CI=0.34-0.96), Megasphaera (HR=0.79, 95% CI=0.64-0.99), Mitsuokella (HR=0.75, 95% CI=0.57-0.99). All-cause mortality was associated with well or moderately differentiated adenocarcinoma (HR=3.84, 95% CI=1.83-8.07), neoadjuvant therapy (HR=4.10, 95% CI=1.40-12.0), tumor stage IV (HR=8.64, 95% CI=3.42-21.8), and presence of venous invasion (HR=2.32, 95% CI=1.08-4.97). Among clinical pathological factors associated with all-cause mortality, Bacteroides abundance significantly interacted with both tumor stage (pinteraction=0.013) and venous invasion (pinteraction=0.001). Conclusion: Our study identified several microbiome features in links with either increasing or decreasing mortality from any causes. Interactions between the gut microbiome and clinical factors might inform insights on how the gut microbiota modulates the effect of clinical factors on CRC prognosis after the curative operation. Further research using postoperative information is needed to confirm our findings. Citation Format: Tung Hoang, Min Jung Kim, Ji Won Park, Seung-Yong Jeong, Aesun Shin. Gut microbiome interacts with clinical characteristics on all-cause mortality of colorectal cancer patients [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 2364.

Airway microbiota and immune mediator relationships differ in obesity and asthma

Asthma and obesity are both complex conditions characterized by chronic inflammation, and obesity-related severe asthma has been associated with differences in the microbiome. However, whether the airway microbiome and microbiota-immune response relationships differ between obese persons with or without nonsevere asthma is unestablished. We compared the airway microbiome and microbiota-immune mediator relationships between obese and nonobese subjects, with and without mild-moderate asthma. We performed cross-sectional analyses of the airway (induced sputum) microbiome and cytokine profiles from blood and sputum using 16S ribosomal RNA gene and internal transcribed spacer region sequencing to profile bacteria and fungi, and multiplex immunoassays. Analysis tools included QIIME 2, linear discriminant analysis effect size (aka LEfSe), Piphillin, and Sparse inverse covariance estimation for ecological association inference (aka SPIEC-EASI). Obesity, irrespective of asthma status, was associated with significant differences in sputum bacterial community structure and composition (unweighted UniFrac permutational analysis of variance, P= .02), including a higher relative abundance of Prevotella, Gemella, and Streptococcus species. Among subjects with asthma, additional differences in sputum bacterial composition and fungal richness were identified between obese and nonobese individuals. Correlation network analyses demonstrated differences between obese and nonobese asthma in relationships between cytokine mediators, and these together with specific airway bacteria involving blood PAI-1, sputum IL-1β, GM-CSF, IL-8, TNF-α, and several Prevotella species. Obesity itself is associated with an altered sputum microbiome, which further differs in those with mild-moderate asthma. The distinct differences in airway microbiota and immune marker relationships in obese asthma suggest potential involvement of airway microbes that may affect mechanisms or outcomes of obese asthma.

Parkinson’s disease progression: Increasing expression of an invariant common core subnetwork

Notable success has been achieved in the study of neurodegenerative conditions using reduction techniques such as principal component analysis (PCA) and sparse inverse covariance estimation (SICE) in positron emission tomography (PET) data despite their widely differing approach. In a recent study of SICE applied to metabolic scans from Parkinson’s disease (PD) patients, we showed that by using PCA to prespecify disease-related partition layers, we were able to optimize maps of functional metabolic connectivity within the relevant networks. Here, we show the potential of SICE, enhanced by disease-specific subnetwork partitions, to identify key regional hubs and their connections, and track their associations in PD patients with increasing disease duration. This approach enabled the identification of a core zone that included elements of the striatum, pons, cerebellar vermis, and parietal cortex and provided a deeper understanding of progressive changes in their connectivity. This subnetwork constituted a robust invariant disease feature that was unrelated to phenotype. Mean expression levels for this subnetwork increased steadily in a group of 70 PD patients spanning a range of symptom durations between 1 and 21 years. The findings were confirmed in a validation sample of 69 patients with up to 32 years of symptoms. The common core elements represent possible targets for disease modification, while their connections to external regions may be better suited for symptomatic treatment.

Microbiological characteristics of different tongue coatings in adults

BackgroundTongue coating is an important health indicator in traditional Chinese medicine (TCM). The tongue coating microbiome can distinguish disease patients from healthy controls. To study the relationship between different types of tongue coatings and health, we analyzed the species composition of different types of tongue coatings and the co-occurrence relationships between microorganisms in Chinese adults.From June 2019 to October 2020, 158 adults from Hangzhou and Shaoxing City, Zhejiang Province, were enrolled. We classified the TCM tongue coatings into four different types: thin white tongue fur (TWF), thin yellow tongue fur (TYF), white greasy tongue fur (WGF), and yellow greasy tongue fur (YGF). Tongue coating specimens were collected and used for 16S rRNA gene sequencing using the Illumina MiSeq system. Wilcoxon rank-sum and permutational multivariate analysis of variance tests were used to analyze the data. The microbial networks in the four types of tongue coatings were inferred independently using sparse inverse covariance estimation for ecological association inference.ResultsThe microbial composition was similar among the different tongue coatings; however, the abundance of microorganisms differed. TWF had a higher abundance of Fusobacterium periodonticum and Neisseria mucosa, the highest α-diversity, and a highly connected community (average degree = 3.59, average closeness centrality = 0.33). TYF had the lowest α-diversity, but the most species in the co-occurrence network diagram (number of nodes = 88). The platelet-to-lymphocyte ratio (PLR) was associated with tongue coating (P = 0.035), and the YGF and TYF groups had higher PLR values. In the co-occurrence network, Aggregatibacter segnis was the “driver species” of the TWF and TYF groups and correlated with C-reactive protein (P < 0.05). Streptococcus anginosus was the “driver species” in the YGF and TWF groups and was positively correlated with body mass index and weight (P < 0.05).ConclusionDifferent tongue coatings have similar microbial compositions but different abundances of certain bacteria. The co-occurrence of microorganisms in the different tongue coatings also varies. The significance of different tongue coatings in TCM theory is consistent with the characteristics and roles of the corresponding tongue-coating microbes. This further supports considering tongue coating as a risk factor for disease.

Reducing instability of inter-subject covariance of FDG uptake networks using structure-weighted sparse estimation approach.

Sparse inverse covariance estimation (SICE) is increasingly utilized to estimate inter-subject covariance of FDG uptake (FDGcov) as proxy of metabolic brain connectivity. However, this statistical method suffers from the lack of robustness in the connectivity estimation. Patterns of FDGcov were observed to be spatially similar with patterns of structural connectivity as obtained from DTI imaging. Based on this similarity, we propose to regularize the sparse estimation of FDGcov using the structural connectivity. We retrospectively analyzed the FDG-PET and DTI data of 26 healthy controls, 41 patients with Alzheimer's disease (AD), and 30 patients with frontotemporal lobar degeneration (FTLD). Structural connectivity matrix derived from DTI data was introduced as a regularization parameter to assign individual penalties to each potential metabolic connectivity. Leave-one-out cross validation experiments were performed to assess the differential diagnosis ability of structure weighted SICE approach. A few approaches of structure weighted were compared with the standard SICE. Compared to the standard SICE, structural weighting has shown more stable performance in the supervised classification, especially in the differentiation AD vs. FTLD (accuracy of 89-90%, while unweighted SICE only 85%). There was a significant positive relationship between the minimum number of metabolic connection and the robustness of the classification accuracy (r = 0.57, P < 0.001). Shuffling experiments showed significant differences between classification score derived with true structural weighting and those obtained by randomized structure (P < 0.05). The structure-weighted sparse estimation can enhance the robustness of metabolic connectivity, which may consequently improve the differentiation of pathological phenotypes.

Altered resting state brain metabolic connectivity in dementia with Lewy bodies.

Although dementia with Lewy bodies (DLB) have Parkinsonism in common with Parkinson's disease (PD) or PD dementia (PDD), they have different neuropathologies that underlie Parkinsonism. Altered brain functional connectivity that may correspond to neuropathology has been reported in PD while never been studied in DLB. To identify the characteristic brain connectivity of Parkinsonism in DLB, we compared the resting state metabolic connectivity in striato-thalamo-cortical (STC) circuit, nigrostriatal pathway, and cerebello-thalamo-cortical motor (CTC) circuit in 27 patients with drug-naïve DLB and 27 age- and sex-matched normal controls using 18F-fluoro-2-deoxyglucose PET. We derived 118 regions of interest using the Automated Anatomical Labeling templates and the Wake Forest University Pick-Atlas. We applied the sparse inverse covariance estimation method to construct the metabolic connectivity matrix. Patients with DLB, with or without Parkinsonism, showed lower inter-regional connectivity between the areas included in the STC circuit (motor cortex–striatum, midbrain–striatum, striatum–globus pallidus, and globus pallidus–thalamus) than the controls. DLB patients with Parkinsonism showed less reduced inter-regional connectivity between the midbrain and the striatum than those without Parkinsonism, and higher inter-regional connectivity between the areas included in the CTC circuit (motor cortex–pons, pons–cerebellum, and cerebellum–thalamus) than those without Parkinsonism and the controls. The resting state metabolic connectivity in the STC circuit may be reduced in DLB. In DLB with Parkinsonism, the CTC circuit and the nigrostriatal pathway may be activated to mitigate Parkinsonism. This difference in the brain connectivity may be a candidate biomarker for differentiating DLB from PD or PDD.

Brain metabolic connectivity reconfiguration in the semantic variant of primary progressive aphasia

Functional network-level alterations in the semantic variant of Primary Progressive Aphasia (sv-PPA) are relevant to understanding the clinical features and the neural spreading of the pathology. We assessed the effect of neurodegeneration on brain systems reorganization in early sv-PPA, using advanced brain metabolic connectivity approaches. Forty-four subjects with sv-PPA and forty-four age-matched healthy controls (HC) were included. We applied two multivariate approaches to [18F]FDG-PET data – i.e., sparse inverse covariance estimation and seed-based interregional correlation analysis – to assess the integrity of (i) the whole-brain metabolic connectivity and (ii) the connectivity of brain regions relevant for cognitive and behavioral functions. Whole-brain analysis revealed a global-scale connectivity reconfiguration in sv-PPA, with widespread changes in metabolic connections of frontal, temporal, and parietal regions. In comparison to HC, the seed-based analysis revealed a) functional isolation of the left anterior temporal lobe (ATL), b) decreases in temporo-occipital connections and contralateral homologous regions, c) connectivity increases to the dorsal parietal cortex from the spared posterior temporal cortex, d) a disruption of the large-scale limbic brain networks. In sv-PPA, the severe functional derangement of the left ATL may lead to an extensive connectivity reconfiguration, encompassing several brain regions, including those not yet affected by neurodegeneration. These findings support the hypothesis that in sv-PPA the focal vulnerability of the core region (i.e., ATL) can potentially drive the widespread cerebral connectivity changes, already present in the early phase.

Sparse Inverse Covariance Estimation for Causal Inference in Process Data Analytics

Causal analysis plays a vital role in determining the underlying relationship among the variables in a system from the data. In this article, the sparse inverse covariance (SIC) estimation is coupled with likelihood score, and a two-step approach is proposed to address the problem of causal analysis. The estimation of SIC matrix for undirected sparse network reconstruction is performed with the <inline-formula> <tex-math notation="LaTeX">$L_{0}$ </tex-math></inline-formula>-norm constraint in the framework of greedy sparse simplex (GSS) algorithm. Furthermore, the GSS algorithm is suitably modified to incorporate the additional constraint of positive semidefiniteness of the inverse covariance matrix. To determine the causal direction among the variables, the likelihood score is computed for the associated variables in the reconstructed network in the second step. The efficacy of the proposed approach for causal analysis is illustrated using numerical examples and an industrial application on prediction of flooding and weeping in a deethanizer column associated with a fluid catalytic cracking unit. From these studies, it is observed that the proposed approach is able to recover causal connections accurately in both cases. Furthermore, the probable reasons for the occurrence of flooding and weeping phenomena in an industrial deethanizer unit are also inferred from the identified causal network.

Reconfigured metabolism brain network in asymptomatic microtubule-associated protein tau mutation carriers: a graph theoretical analysis

BackgroundStudies exploring topological properties of the metabolic network during the presymptomatic stage of genetic frontotemporal dementia (FTD) are scarce. However, such knowledge is important for understanding brain function and disease pathogenesis. Therefore, we aimed to explore FTD-specific patterns of metabolism topology reconfiguration in microtubule-associated protein tau (MAPT) mutation carriers before the onset of symptoms.MethodsSix asymptomatic carriers of the MAPT P301L mutation were compared with 12 non-carriers who all belonged to the same family of FTD. For comparison, we included 32 behavioral variant FTD (bvFTD) patients and 33 unrelated healthy controls. Each participant underwent neuropsychological assessments, genetic testing, and a hybrid positron emission tomography (PET)/magnetic resonance imaging (MRI) scan. Voxel-wise gray matter volumes and standardized uptake value ratios were calculated and compared for structural MRI and fluorodeoxyglucose (FDG)-PET, separately. The sparse inverse covariance estimation method (SICE) was applied to topological properties and metabolic connectomes of brain functional networks derived from 18F-FDG PET/MRI data. Independent component analysis was used to explore the metabolic connectivity of the salience (SN) and default mode networks (DMN).ResultsThe asymptomatic MAPT carriers performed normal global parameters of the metabolism network, whereas bvFTD patients did not. However, we revealed lost hubs in the ventromedial prefrontal, orbitofrontal, and anterior cingulate cortices and reconfigured hubs in the anterior insula, precuneus, and posterior cingulate cortex in asymptomatic carriers compared with non-carriers, which overlapped with the comparisons between bvFTD patients and controls. Similarly, significant differences in local parameters of these nodes were present between asymptomatic carriers and non-carriers. The reduction in the connectivity of lost hub regions and the enhancement of connectivity between reconfigured hubs and components of the frontal cortex were marked during the asymptomatic stage. Metabolic connectivity within the SN and DMN was enhanced in asymptomatic carriers compared with non-mutation carriers but reduced in bvFTD patients relative to controls.ConclusionsOur findings showed that metabolism topology reconfiguration, characterized by the earliest involvement of medial prefrontal areas and active compensation in task-related regions, was present in the presymptomatic phase of genetic FTD with MAPT mutation, which may be used as an imaging biomarker of increased risk of FTD.

Mapping covariance in brain FDG uptake to structural connectivity

PurposeInter-subject covariance of regional 18F-fluorodeoxyglucose (FDG) PET measures (FDGcov) as proxy of brain connectivity has been gaining an increasing acceptance in the community. Yet, it is still unclear to what extent FDGcov is underlied by actual structural connectivity via white matter fiber tracts. In this study, we quantified the degree of spatial overlap between FDGcov and structural connectivity networks.MethodsWe retrospectively analyzed neuroimaging data from 303 subjects, both patients with suspected neurodegenerative disorders and healthy individuals. For each subject, structural magnetic resonance, diffusion tensor imaging, and FDG-PET data were available. The images were spatially normalized to a standard space and segmented into 62 anatomical regions using a probabilistic atlas. Sparse inverse covariance estimation was employed to estimate FDGcov. Structural connectivity was measured by streamline tractography through fiber assignment by continuous tracking.ResultsFor the whole brain, 55% of detected connections were found to be convergent, i.e., present in both FDGcov and structural networks. This metric for random networks was significantly lower, i.e., 12%. Convergent were 80% of intralobe connections and only 30% of interhemispheric interlobe connections.ConclusionStructural connectivity via white matter fiber tracts is a relevant substrate of FDGcov, underlying around a half of connections at the whole brain level. Short-range white matter tracts appear to be a major substrate of intralobe FDGcov connections.

Dynamic Portfolio Management with Machine Learning

We present a structured portfolio optimization framework with sparse inverse covariance estimation and an attention-based LSTM network that exploits machine learning (deep learning) techniques. We shrink Wishart volatility towards a Graphical Lasso initial covariance estimator and solve the portfolio optimization using a fast coordinate descent algorithm with regularization determined using a genetic algorithm. We further introduce a novel portfolio shrinkage rule using an attention-based Long-Short-Term-Memory (LSTM) network, allowing a formal selection of reference portfolios where the network forecasts future performance based on predetermined out-of-sample monthly certainty equivalent return. We reduce the dimension of successful candidates and then linearly combine them. When nested within a minimum-variance, Bayes-Stein shrinkage, Black-Litterman portfolio framework with four types of weight constraints based on no-short-selling, upper, lower-generalized variance-based restrictions, our approach delivers a clear improvement over the baseline sample-based minimum-variance portfolio and claims superiority over 11 GARCH models used to forecast covariances, as well as a minimum-variance combination of all dynamic optimization models. We provide an illustrative example based on optimal diversification across hedge fund strategies. Robustness checks show our application of sparse covariance dominates the use of a dimension reduction algorithm for Wishart covariance forecasting.

Spectral guided sparse inverse covariance estimation of metabolic networks in Parkinson's disease

In neurodegenerative disorders, a clearer understanding of the underlying aberrant networks facilitates the search for effective therapeutic targets and potential cures. [18F]-fluorodeoxyglucose (FDG) positron emission tomography (PET) imaging data of brain metabolism reflects the distribution of glucose consumption known to be directly related to neural activity. In FDG PET resting-state metabolic data, characteristic disease-related patterns have been identified in group analysis of various neurodegenerative conditions using principal component analysis of multivariate spatial covariance. Notably, among several parkinsonian syndromes, the identified Parkinson's disease-related pattern (PDRP) has been repeatedly validated as an imaging biomarker of PD in independent groups worldwide. Although the primary nodal associations of this network are known, its connectivity is not fully understood. Here, we describe a novel approach to elucidate functional principal component (PC) network connections by performing graph theoretical sparse network derivation directly within the disease relevant PC partition layer of the whole brain data rather than by searching for associations retrospectively in whole brain sparse representations. Using sparse inverse covariance estimation of each overlapping PC partition layer separately, a single coherent network is detected for each layer in contrast to more spatially modular segmentation in whole brain data analysis. Using this approach, the major nodal hubs of the PD disease network are identified and their characteristic functional pathways are clearly distinguished within the basal ganglia, midbrain and parietal areas. Network associations are further clarified using Laplacian spectral analysis of the adjacency matrices. In addition, the innate discriminative capacity of the eigenvector centrality of the graph derived networks in differentiating PD versus healthy external data provides evidence of their validity.

Inference and Analysis of SPIEC-EASI Microbiome Networks.

Network analysis facilitates examination of the interactions between different populations in a community. It can provide a range of metrics describing the social characteristics of each population and emergent structural properties of the community, which may be used to address novel ecological questions. Using a publicly available dataset, this chapter provides point-by-point code and instructions to infer and analyze a SPIEC-EASI (SParse InversE Covariance Estimation for Ecological Association Inference) network using free, open source software (R and Gephi).

Microbial Interaction Network Estimation via Bias-Corrected Graphical Lasso

With the increasing availability of microbiome 16S data, network estimation has become a useful approach to studying the interactions between microbial taxa. Network estimation on a set of variables is frequently explored using graphical models, in which the relationship between two variables is modeled via their conditional dependency given the other variables. Various methods for sparse inverse covariance estimation have been proposed to estimate graphical models in the high-dimensional setting, including graphical lasso. However, current methods do not address the compositional count nature of microbiome data, where abundances of microbial taxa are not directly measured, but are reflected by the observed counts in an error-prone manner. Adding to the challenge is that the sum of the counts within each sample, termed “sequencing depth,” is an experimental technicality that carries no biological information but can vary drastically across samples. To address these issues, we develop a new approach to network estimation, called BC-GLASSO (bias-corrected graphical lasso), which models the microbiome data using a logistic normal multinomial distribution with the sequencing depths explicitly incorporated, corrects the bias of the naive empirical covariance estimator arising from the heterogeneity in sequencing depths, and builds the inverse covariance estimator via graphical lasso. We demonstrate the advantage of BC-GLASSO over current approaches to microbial interaction network estimation under a variety of simulation scenarios. We also illustrate the efficacy of our method in an application to a human microbiome data set.

Evaluating the significance of contact maps in low-homology protein modeling using contact-assisted threading

The development of improved threading algorithms for remote homology modeling is a critical step forward in template-based protein structure prediction. We have recently demonstrated the utility of contact information to boost protein threading by developing a new contact-assisted threading method. However, the nature and extent to which the quality of a predicted contact map impacts the performance of contact-assisted threading remains elusive. Here, we systematically analyze and explore this interdependence by employing our newly-developed contact-assisted threading method over a large-scale benchmark dataset using predicted contact maps from four complementary methods including direct coupling analysis (mfDCA), sparse inverse covariance estimation (PSICOV), classical neural network-based meta approach (MetaPSICOV), and state-of-the-art ultra-deep learning model (RaptorX). Experimental results demonstrate that contact-assisted threading using high-quality contacts having the Matthews Correlation Coefficient (MCC) ≥ 0.5 improves threading performance in nearly 30% cases, while low-quality contacts with MCC <0.35 degrades the performance for 50% cases. This holds true even in CASP13 dataset, where threading using high-quality contacts (MCC ≥ 0.5) significantly improves the performance of 22 instances out of 29. Collectively, our study uncovers the mutual association between the quality of predicted contacts and its possible utility in boosting threading performance for improving low-homology protein modeling.

A dual spectral projected gradient method for log-determinant semidefinite problems

We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem with linear constraints and propose a spectral projected gradient method for the dual problem. Our method is based on alternate projections on the intersection of two convex sets, which first projects onto the box constraints and then onto a set defined by a linear matrix inequality. By exploiting structures of the two projections, we show that the same convergence properties can be obtained for the proposed method as Birgin’s method where the exact orthogonal projection onto the intersection of two convex sets is performed. Using the convergence properties, we prove that the proposed algorithm attains the optimal value or terminates in a finite number of iterations. The efficiency of the proposed method is illustrated with the numerical results on randomly generated synthetic/deterministic data and gene expression data, in comparison with other methods including the inexact primal–dual path-following interior-point method, the Newton-CG primal proximal-point algorithm, the adaptive spectral projected gradient method, and the adaptive Nesterov’s smooth method. For the gene expression data, our results are compared with the quadratic approximation for sparse inverse covariance estimation method. We show that our method outperforms the other methods in obtaining a better objective value fast.

Sparse inverse covariance estimation for high-throughput microRNA sequencing data in the Poisson log-normal graphical model

ABSTRACTWe introduce a one-step EM algorithm to estimate the graphical structure in a Poisson-Log-Normal graphical model. This procedure is equivalent to a normality transformation that makes the problem of identifying relationships in high-throughput microRNA (miRNA) sequence data feasible. The Poisson-log-normal model moreover allows us to directly account for known overdispersion relationships present in this data set. We show that our EM algorithm provides a provable increase in performance in determining the network structure. The model is shown to provide an increase in performance in simulation settings over a range of network structures. The model is applied to high-throughput miRNA sequencing data from patients with breast cancer from The Cancer Genome Atlas (TCGA). By selecting the most highly connected miRNA molecules in the fitted network we find that nearly all of them are known to be involved in the regulation of breast cancer.