Scalable Bayesian variable selection for structured high-dimensional data

Bayesian mixed model inference for genetic association under related samples with brain network phenotype

Genetic association studies for brain connectivity phenotypes have gained prominence due to advances in noninvasive imaging techniques and quantitative genetics. Brain connectivity traits, characterized by network configurations and unique biological structures, present distinct challenges compared to other quantitative phenotypes. Furthermore, the presence of sample relatedness in the most imaging genetics studies limits the feasibility of adopting existing network-response modeling. In this article, we fill this gap by proposing a Bayesian network-response mixed-effect model that considers a network-variate phenotype and incorporates population structures including pedigrees and unknown sample relatedness. To accommodate the inherent topological architecture associated with the genetic contributions to the phenotype, we model the effect components via a set of effect network configurations and impose an inter-network sparsity and intra-network shrinkage to dissect the phenotypic network configurations affected by the risk genetic variant. A Markov chain Monte Carlo (MCMC) algorithm is further developed to facilitate uncertainty quantification. We evaluate the performance of our model through extensive simulations. By further applying the method to study, the genetic bases for brain structural connectivity using data from the Human Connectome Project with excessive family structures, we obtain plausible and interpretable results. Beyond brain connectivity genetic studies, our proposed model also provides a general linear mixed-effect regression framework for network-variate outcomes.

Group lasso priors for Bayesian accelerated failure time models with left-truncated and interval-censored data

An important task in health research is to characterize time-to-event outcomes such as disease onset or mortality in terms of a potentially high-dimensional set of risk factors. For example, prospective cohort studies of Alzheimer's disease (AD) typically enroll older adults for observation over several decades to assess the long-term impact of genetic and other factors on cognitive decline and mortality. The accelerated failure time model is particularly well-suited to such studies, structuring covariate effects as "horizontal" changes to the survival quantiles that conceptually reflect shifts in the outcome distribution due to lifelong exposures. However, this modeling task is complicated by the enrollment of adults at differing ages, and intermittent follow-up visits leading to interval-censored outcome information. Moreover, genetic and clinical risk factors are not only high-dimensional, but characterized by underlying grouping structures, such as by function or gene location. Such grouped high-dimensional covariates require shrinkage methods that directly acknowledge this structure to facilitate variable selection and estimation. In this paper, we address these considerations directly by proposing a Bayesian accelerated failure time model with a group-structured lasso penalty, designed for left-truncated and interval-censored time-to-event data. We develop an R package with a Markov chain Monte Carlo sampler for estimation. We present a simulation study examining the performance of this method relative to an ordinary lasso penalty and apply the proposed method to identify groups of predictive genetic and clinical risk factors for AD in the Religious Orders Study and Memory and Aging Project prospective cohort studies of AD and dementia.

Single-cell biclustering for cell-specific transcriptomic perturbation detection in AD progression

The pathogenesis of Alzheimer disease (AD) involves complex gene regulatory changes across different cell types. To help decipher this complexity, we introduce single-cell Bayesian biclustering (scBC), a framework for identifying cell-specific gene network biomarkers in scRNA and snRNA-seq data. Through biclustering, scBC enables the analysis of perturbations in functional gene modules at the single-cell level. Applying the scBC framework to AD snRNA-seq data reveals the perturbations within gene modules across distinct cell groups and sheds light on gene-cell correlations during AD progression. Notably, our method helps to overcome common challenges in single-cell data analysis, including batch effects and dropout events. Incorporating prior knowledge further enables the framework to yield more biologically interpretable results. Comparative analyses on simulated and real-world datasets demonstrate the precision and robustness of our approach compared to other state-of-the-art biclustering methods. scBC holds potential for unraveling the mechanisms underlying polygenic diseases characterized by intricate gene coexpression patterns.

Accounting for network noise in graph-guided Bayesian modeling of structured high-dimensional data

There is a growing body of literature on knowledge-guided statistical learning methods for analysis of structured high-dimensional data (such as genomic and transcriptomic data) that can incorporate knowledge of underlying networks derived from functional genomics and functional proteomics. These methods have been shown to improve variable selection and prediction accuracy and yield more interpretable results. However, these methods typically use graphs extracted from existing databases or rely on subject matter expertise, which are known to be incomplete and may contain false edges. To address this gap, we propose a graph-guided Bayesian modeling framework to account for network noise in regression models involving structured high-dimensional predictors. Specifically, we use 2 sources of network information, including the noisy graph extracted from existing databases and the estimated graph from observed predictors in the dataset at hand, to inform the model for the true underlying network via a latent scale modeling framework. This model is coupled with the Bayesian regression model with structured high-dimensional predictors involving an adaptive structured shrinkage prior. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling. We demonstrate the advantages of our method over existing methods in simulations, and through analyses of a genomics dataset and another proteomics dataset for Alzheimer's disease.

Incorporating graph information in Bayesian factor analysis with robust and adaptive shrinkage priors

There has been an increasing interest in decomposing high-dimensional multi-omics data into a product of low-rank and sparse matrices for the purpose of dimension reduction and feature engineering. Bayesian factor models achieve such low-dimensional representation of the original data through different sparsity-inducing priors. However, few of these models can efficiently incorporate the information encoded by the biological graphs, which has been already proven to be useful in many analysis tasks. In this work, we propose a Bayesian factor model with novel hierarchical priors, which incorporate the biological graph knowledge as a tool of identifying a group of genes functioning collaboratively. The proposed model therefore enables sparsity within networks by allowing each factor loading to be shrunk adaptively and by considering additional layers to relate individual shrinkage parameters to the underlying graph information, both of which yield a more accurate structure recovery of factor loadings. Further, this new priors overcome the phase transition phenomenon, in contrast to existing graph-incorporated approaches, so that it is robust to noisy edges that are inconsistent with the actual sparsity structure of the factor loadings. Finally, our model can handle both continuous and discrete data types. The proposed method is shown to outperform several existing factor analysis methods through simulation experiments and real data analyses.

Integrative Bayesian tensor regression for imaging genetics applications

Identifying biomarkers for Alzheimer's disease with a goal of early detection is a fundamental problem in clinical research. Both medical imaging and genetics have contributed informative biomarkers in literature. To further improve the performance, recently, there is an increasing interest in developing analytic approaches that combine data across modalities such as imaging and genetics. However, there are limited methods in literature that are able to systematically combine high-dimensional voxel-level imaging and genetic data for accurate prediction of clinical outcomes of interest. Existing prediction models that integrate imaging and genetic features often use region level imaging summaries, and they typically do not consider the spatial configurations of the voxels in the image or incorporate the dependence between genes that may compromise prediction ability. We propose a novel integrative Bayesian scalar-on-image regression model for predicting cognitive outcomes based on high-dimensional spatially distributed voxel-level imaging data, along with correlated transcriptomic features. We account for the spatial dependencies in the imaging voxels via a tensor approach that also enables massive dimension reduction to address the curse of dimensionality, and models the dependencies between the transcriptomic features via a Graph-Laplacian prior. We implement this approach via an efficient Markov chain Monte Carlo (MCMC) computation strategy. We apply the proposed method to the analysis of longitudinal ADNI data for predicting cognitive scores at different visits by integrating voxel-level cortical thickness measurements derived from T1w-MRI scans and transcriptomics data. We illustrate that the proposed imaging transcriptomics approach has significant improvements in prediction compared to prediction using a subset of features from only one modality (imaging or genetics), as well as when using imaging and transcriptomics features but ignoring the inherent dependencies between the features. Our analysis is one of the first to conclusively demonstrate the advantages of prediction based on combining voxel-level cortical thickness measurements along with transcriptomics features, while accounting for inherent structural information.

Integrative Learning of Structured High-Dimensional Data from Multiple Datasets

Integrative learning of multiple datasets has the potential to mitigate the challenge of small n and large p that is often encountered in analysis of big biomedical data such as genomics data. Detection of weak yet important signals can be enhanced by jointly selecting features for all datasets. However, the set of important features may not always be the same across all datasets. Although some existing integrative learning methods allow heterogeneous sparsity structure where a subset of datasets can have zero coefficients for some selected features, they tend to yield reduced efficiency, reinstating the problem of losing weak important signals. We propose a new integrative learning approach which can not only aggregate important signals well in homogeneous sparsity structure, but also substantially alleviate the problem of losing weak important signals in heterogeneous sparsity structure. Our approach exploits a priori known graphical structure of features and encourages joint selection of features that are connected in the graph. Integrating such prior information over multiple datasets enhances the power, while also accounting for the heterogeneity across datasets. Theoretical properties of the proposed method are investigated. We also demonstrate the limitations of existing approaches and the superiority of our method using a simulation study and analysis of gene expression data from ADNI.

Integrative analysis of multi-omics and imaging data with incorporation of biological information via structural Bayesian factor analysis

MOTIVATION

With the rapid development of modern technologies, massive data are available for the systematic study of Alzheimer's disease (AD). Though many existing AD studies mainly focus on single-modality omics data, multi-omics datasets can provide a more comprehensive understanding of AD. To bridge this gap, we proposed a novel structural Bayesian factor analysis framework (SBFA) to extract the information shared by multi-omics data through the aggregation of genotyping data, gene expression data, neuroimaging phenotypes and prior biological network knowledge. Our approach can extract common information shared by different modalities and encourage biologically related features to be selected, guiding future AD research in a biologically meaningful way.

METHOD

Our SBFA model decomposes the mean parameters of the data into a sparse factor loading matrix and a factor matrix, where the factor matrix represents the common information extracted from multi-omics and imaging data. Our framework is designed to incorporate prior biological network information. Our simulation study demonstrated that our proposed SBFA framework could achieve the best performance compared with the other state-of-the-art factor-analysis-based integrative analysis methods.

RESULTS

We apply our proposed SBFA model together with several state-of-the-art factor analysis models to extract the latent common information from genotyping, gene expression and brain imaging data simultaneously from the ADNI biobank database. The latent information is then used to predict the functional activities questionnaire score, an important measurement for diagnosis of AD quantifying subjects' abilities in daily life. Our SBFA model shows the best prediction performance compared with the other factor analysis models.

AVAILABILITY

Code are publicly available at https://github.com/JingxuanBao/SBFA.

CONTACT

qlong@upenn.edu.

Genetic underpinnings of brain structural connectome for young adults

With distinct advantages in power over behavioral phenotypes, brain imaging traits have become emerging endophenotypes to dissect molecular contributions to behaviors and neuropsychiatric illnesses. Among different imaging features, brain structural connectivity (i.e., structural connectome) which summarizes the anatomical connections between different brain regions is one of the most cutting edge while under-investigated traits; and the genetic influence on the structural connectome variation remains highly elusive. Relying on a landmark imaging genetics study for young adults, we develop a biologically plausible brain network response shrinkage model to comprehensively characterize the relationship between high dimensional genetic variants and the structural connectome phenotype. Under a unified Bayesian framework, we accommodate the topology of brain network and biological architecture within the genome; and eventually establish a mechanistic mapping between genetic biomarkers and the associated brain sub-network units. An efficient expectation-maximization algorithm is developed to estimate the model and ensure computing feasibility. In the application to the Human Connectome Project Young Adult (HCP-YA) data, we establish the genetic underpinnings which are highly interpretable under functional annotation and brain tissue eQTL analysis, for the brain white matter tracts connecting the hippocampus and two cerebral hemispheres. We also show the superiority of our method in extensive simulations.

Graph-guided Bayesian SVM with Adaptive Structured Shrinkage Prior for High-dimensional Data

Support vector machine (SVM) is a popular classification method for the analysis of a wide range of data including big biomedical data. Many SVM methods with feature selection have been developed under the frequentist regularization or Bayesian shrinkage frameworks. On the other hand, the value of incorporating a priori known biological knowledge, such as those from functional genomics and functional proteomics, into statistical analysis of -omic data has been recognized in recent years. Such biological information is often represented by graphs. We propose a novel method that assigns Laplace priors to the regression coefficients and incorporates the underlying graph information via a hyper-prior for the shrinkage parameters in the Laplace priors. This enables smoothing of shrinkage parameters for connected variables in the graph and conditional independence between shrinkage parameters for disconnected variables. Extensive simulations demonstrate that our proposed methods achieve the best performance compared to the other existing SVM methods in terms of prediction accuracy. The proposed method are also illustrated in analysis of genomic data from cancer studies, demonstrating its advantage in generating biologically meaningful results and identifying potentially important features.

Bayesian sparse heritability analysis with high-dimensional neuroimaging phenotypes

Heritability analysis plays a central role in quantitative genetics to describe genetic contribution to human complex traits and prioritize downstream analyses under large-scale phenotypes. Existing works largely focus on modeling single phenotype and currently available multivariate phenotypic methods often suffer from scaling and interpretation. In this article, motivated by understanding how genetic underpinning impacts human brain variation, we develop an integrative Bayesian heritability analysis to jointly estimate heritabilities for high-dimensional neuroimaging traits. To induce sparsity and incorporate brain anatomical configuration, we impose hierarchical selection among both regional and local measurements based on brain structural network and voxel dependence. We also use a nonparametric Dirichlet process mixture model to realize grouping among single nucleotide polymorphism-associated phenotypic variations, providing biological plausibility. Through extensive simulations, we show the proposed method outperforms existing ones in heritability estimation and heritable traits selection under various scenarios. We finally apply the method to two large-scale imaging genetics datasets: the Alzheimer's Disease Neuroimaging Initiative and United Kingdom Biobank and show biologically meaningful results.

Bayesian generalized biclustering analysis via adaptive structured shrinkage

Biclustering techniques can identify local patterns of a data matrix by clustering feature space and sample space at the same time. Various biclustering methods have been proposed and successfully applied to analysis of gene expression data. While existing biclustering methods have many desirable features, most of them are developed for continuous data and few of them can efficiently handle -omics data of various types, for example, binomial data as in single nucleotide polymorphism data or negative binomial data as in RNA-seq data. In addition, none of existing methods can utilize biological information such as those from functional genomics or proteomics. Recent work has shown that incorporating biological information can improve variable selection and prediction performance in analyses such as linear regression and multivariate analysis. In this article, we propose a novel Bayesian biclustering method that can handle multiple data types including Gaussian, Binomial, and Negative Binomial. In addition, our method uses a Bayesian adaptive structured shrinkage prior that enables feature selection guided by existing biological information. Our simulation studies and application to multi-omics datasets demonstrate robust and superior performance of the proposed method, compared to other existing biclustering methods.

Bayesian Network Marker Selection via the Thresholded Graph Laplacian Gaussian Prior

Selecting informative nodes over large-scale networks becomes increasingly important in many research areas. Most existing methods focus on the local network structure and incur heavy computational costs for the large-scale problem. In this work, we propose a novel prior model for Bayesian network marker selection in the generalized linear model (GLM) framework: the Thresholded Graph Laplacian Gaussian (TGLG) prior, which adopts the graph Laplacian matrix to characterize the conditional dependence between neighboring markers accounting for the global network structure. Under mild conditions, we show the proposed model enjoys the posterior consistency with a diverging number of edges and nodes in the network. We also develop a Metropolis-adjusted Langevin algorithm (MALA) for efficient posterior computation, which is scalable to large-scale networks. We illustrate the superiorities of the proposed method compared with existing alternatives via extensive simulation studies and an analysis of the breast cancer gene expression dataset in the Cancer Genome Atlas (TCGA).

GRIA: Graphical Regularization for Integrative Analysis

Integrative analysis jointly analyzes multiple data sets to overcome curse of dimensionality. It can detect important but weak signals by jointly selecting features for all data sets, but unfortunately the sets of important features are not always the same for all data sets. Variations which allows heterogeneous sparsity structure-a subset of data sets can have a zero coefficient for a selected feature-have been proposed, but it compromises the effect of integrative analysis recalling the problem of losing weak important signals. We propose a new integrative analysis approach which not only aggregates weak important signals well in homogeneity setting but also substantially alleviates the problem of losing weak important signals in heterogeneity setting. Our approach exploits a priori known graphical structure of features by forcing joint selection of adjacent features, and integrating such information over multiple data sets can increase the power while taking into account the heterogeneity across data sets. We confirm the problem of existing approaches and demonstrate the superiority of our method through a simulation study and an application to gene expression data from ADNI.

Integrative analysis of genetical genomics data incorporating network structures

In a living organism, tens of thousands of genes are expressed and interact with each other to achieve necessary cellular functions. Gene regulatory networks contain information on regulatory mechanisms and the functions of gene expressions. Thus, incorporating network structures, discerned either through biological experiments or statistical estimations, could potentially increase the selection and estimation accuracy of genes associated with a phenotype of interest. Here, we considered a gene selection problem using gene expression data and the graphical structures found in gene networks. Because gene expression measurements are intermediate phenotypes between a trait and its associated genes, we adopted an instrumental variable regression approach. We treated genetic variants as instrumental variables to address the endogeneity issue. We proposed a two-step estimation procedure. In the first step, we applied the LASSO algorithm to estimate the effects of genetic variants on gene expression measurements. In the second step, the projected expression measurements obtained from the first step were treated as input variables. A graph-constrained regularization method was adopted to improve the efficiency of gene selection and estimation. We theoretically showed the selection consistency of the estimation method and derived the L ∞ bound of the estimates. Simulation and real data analyses were conducted to demonstrate the effectiveness of our method and to compare it with its counterparts.

Bayesian Non-linear Support Vector Machine for High-Dimensional Data with Incorporation of Graph Information on Features

Support vector machine (SVM) is a popular classification method for analysis of high dimensional data such as genomics data. Recently a number of linear SVM methods have been developed to achieve feature selection through either frequentist regularization or Bayesian shrinkage, but the linear assumption may not be plausible for many real applications. In addition, recent work has demonstrated that incorporating known biological knowledge, such as those from functional genomics, into the statistical analysis of genomic data offers great promise of improved predictive accuracy and feature selection. Such biological knowledge can often be represented by graphs. In this article, we propose a novel knowledge-guided nonlinear Bayesian SVM approach for analysis of high-dimensional data. Our model uses graph information that represents the relationship among the features to guide feature selection. To achieve knowledge-guided feature selection, we assign an Ising prior to the indicators representing inclusion/exclusion of the features in the model. An efficient MCMC algorithm is developed for posterior inference. The performance of our method is evaluated and compared with several penalized linear SVM and the standard kernel SVM method in terms of prediction and feature selection in extensive simulation studies. Also, analyses of genomic data from a cancer study show that our method yields a more accurate prediction model for patient survival and reveals biologically more meaningful results than the existing methods.

Knowledge-Guided Biclustering via Sparse Variational EM Algorithm

A biclustering in the analysis of a gene expression data matrix, for example, is defined as a set of biclusters where each bicluster is a group of genes and a group of samples for which the genes are differentially expressed. Although many data mining approaches for biclustering exist in the literature, only few are able to incorporate prior knowledge to the analysis, which can lead to great improvements in terms of accuracy and interpretability, and all are limited in handling discrete data types. We propose a generalized biclustering approach that can be used for integrative analysis of multi-omics data with different data types. Our method is capable of utilizing biological information that can be represented by graph such as functional genomics and functional proteomics and accommodating a combination of continuous and discrete data types. The proposed method builds on a generalized Bayesian factor analysis framework and a variational EM approach is used to obtain parameter estimates, where the latent quantities in the loglikelihood are iteratively imputed by their conditional expectations. The biclusters are retrieved via the sparse estimates of the factor loadings and the conditional expectation of the latent factors. In order to obtain the sparse conditional expectation of the latent factors, a novel sparse variational EM algorithm is used. We demonstrate the superiority of our method over several existing biclustering methods in extensive simulation experiements and in integrative analysis of multi-omics data.

Knowledge-Guided Statistical Learning Methods for Analysis of High-Dimensional -Omics Data in Precision Oncology

High-dimensional -omics data such as genomic, transcriptomic, and metabolomic data offer great promise in advancing precision medicine. In particular, such data have enabled the investigation of complex diseases such as cancer at an unprecedented scale and in multiple dimensions. However, a number of analytical challenges complicate analysis of high-dimensional -omics data. One is the growing recognition that complex diseases such as cancer are multifactorial and may be attributed to harmful changes on multiple -omics levels and on the pathway level. When individual genes in an important pathway have relatively weak signals, it can be challenging to detect them on their own, but the aggregated signal in the pathway can be considerably stronger and hence easier to detect with the same sample size. To address these challenges, there is a growing body of literature on knowledge-guided statistical learning methods for analysis of high-dimensional -omics data that can incorporate biological knowledge such as functional genomics and functional proteomics. These methods have been shown to improve predication and classification accuracy and yield biologically more interpretable results compared with statistical learning methods that do not use biological knowledge. In this review, we survey current knowledge-guided statistical learning methods, including both supervised learning and unsupervised learning, and their applications to precision oncology, and we discuss future research directions.

Knowledge-Guided Bayesian Support Vector Machine for High-Dimensional Data with Application to Analysis of Genomics Data

Support vector machine (SVM) is a popular classification method for the analysis of wide range of data including big data. Many SVM methods with feature selection have been developed under frequentist regularization or Bayesian shrinkage frameworks. On the other hand, the importance of incorporating a priori known biological knowledge, such as gene pathway information which stems from the gene regulatory network, into the statistical analysis of genomic data has been recognized in recent years. In this article, we propose a new Bayesian SVM approach that enables the feature selection to be guided by the knowledge on the graphical structure among predictors. The proposed method uses the spike-and-slab prior for feature selection, combined with the Ising prior that encourages group-wise selection of the predictors adjacent to each other on the known graph. Gibbs sampling algorithm is used for Bayesian inference. The performance of our method is evaluated and compared with existing SVM methods in terms of prediction and feature selection in extensive simulation settings. In addition, our method is illustrated in the analysis of genomic data from a cancer study, demonstrating its advantage in generating biologically meaningful results and identifying potentially important features.

Generalized Bayesian Factor Analysis for Integrative Clustering with Applications to Multi-Omics Data

Integrative clustering is a clustering approach for multiple datasets, which provide different views of a common group of subjects. It enables analyzing multi-omics data jointly to, for example, identify the subtypes of diseases, cells, and so on, capturing the complex underlying biological processes more precisely. On the other hand, there has been a great deal of interest in incorporating the prior structural knowledge on the features into statistical analyses over the past decade. The knowledge on the gene regulatory network (pathways) can potentially be incorporated into many genomic studies. In this paper, we propose a novel integrative clustering method which can incorporate the prior graph knowledge. We first develop a generalized Bayesian factor analysis (GBFA) framework, a sparse Bayesian factor analysis which can take into account the graph information. Our GBFA framework employs the spike and slab lasso (SSL) prior to impose sparsity on the factor loadings and the Markov random field (MRF) prior to encourage smoothing over the adjacent factor loadings, which establishes a unified shrinkage adaptive to the loading size and the graph structure. Then, we use the framework to extend iCluster+, a factor analysis based integrative clustering approach. A novel variational EM algorithm is proposed to efficiently estimate the MAP estimator for the factor loadings. Extensive simulation studies and the application to the NCI60 cell line dataset demonstrate that the propose method is superior and delivers more biologically meaningful outcomes.

Integrative Bayesian analysis of brain functional networks incorporating anatomical knowledge

Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization by integrating information on both brain structure and function. In particular, incorporating anatomical knowledge leads to desirable outcomes such as increased accuracy in brain network estimates and greater reproducibility of topological features across scanning sessions. Despite the clear advantages, major challenges persist in integrative analyses including an incomplete understanding of the structure-function relationship and inaccuracies in mapping anatomical structures due to inherent deficiencies in existing imaging technology. This calls for the development of advanced network modeling tools that appropriately incorporate anatomical structure in constructing brain functional networks. We propose a hierarchical Bayesian Gaussian graphical modeling approach which models the brain functional networks via sparse precision matrices whose degree of edge specific shrinkage is a random variable that is modeled using both anatomical structure and an independent baseline component. The proposed approach adaptively shrinks functional connections and flexibly identifies functional connections supported by structural connectivity knowledge. This enables robust brain network estimation even in the presence of misspecified anatomical knowledge, while accommodating heterogeneity in the structure-function relationship. We implement the approach via an efficient optimization algorithm which yields maximum a posteriori estimates. Extensive numerical studies involving multiple functional network structures reveal the clear advantages of the proposed approach over competing methods in accurately estimating brain functional connectivity, even when the anatomical knowledge is misspecified up to a certain degree. An application of the approach to data from the Philadelphia Neurodevelopmental Cohort (PNC) study reveals gender based connectivity differences across multiple age groups, and higher reproducibility in the estimation of network metrics compared to alternative methods.