Integrative network modeling of data arising from multiple genomic platforms provides insight into the holistic picture of the interactive system, as well as the flow of information across many disease domains including cancer. The basic data structure consists of a sequence of hierarchically ordered datasets for each individual subject, which facilitates integration of diverse inputs, such as genomic, transcriptomic, and proteomic data. A primary analytical task in such contexts is to model the layered architecture of networks where the vertices can be naturally partitioned into ordered layers, dictated by multiple platforms, and exhibit both undirected and directed relationships. We propose a multi-layered Gaussian graphical model (mlGGM) to investigate conditional independence structures in such multi-level genomic networks in human cancers. We implement a Bayesian node-wise selection (BANS) approach based on variable selection techniques that coherently accounts for the multiple types of dependencies in mlGGM; this flexible strategy exploits edge-specific prior knowledge and selects sparse and interpretable models. Through simulated data generated under various scenarios, we demonstrate that BANS outperforms other existing multivariate regression-based methodologies. Our integrative genomic network analysis for key signaling pathways across multiple cancer types highlights commonalities and differences of p53 integrative networks and epigenetic effects of BRCA2 on p53 and its interaction with T68 phosphorylated CHK2, that may have translational utilities of finding biomarkers and therapeutic targets.
We propose a novel way of modelling time-varying networks, by inducing two-way sparsity on local models of node connectivity. This two-way sparsity separately promotes sparsity across time and sparsity across variables (within time). Separation of these two types of sparsity is achieved through a novel prior structure, which draws on ideas from the Bayesian lasso and from copula modelling. We provide an efficient implementation of the proposed model via a Gibbs sampler, and we apply the model to data from neural development. In doing so, we demonstrate that the proposed model is able to identi…
Rapid advancements in collection and dissemination of multi-platform molecular and genomics data has resulted in enormous opportunities to aggregate such data in order to understand, prevent, and treat human diseases. While significant improvements have been made in multi-omic data integration methods to discover biological markers and mechanisms underlying both prognosis and treatment, the precise cellular functions governing these complex mechanisms still need detailed and data-driven de-novo evaluations. We propose a framework called Functional Integrative Bayesian Analysis of High-dimensio…
Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm based upon Evolutionary Monte Carlo and designed to work under the "large p, small n" paradigm, thus making fully Bayesian multivariate analysis feasible, for example, in genetics/genomics experiments. Two real data examples in genomics are presented, demonstrating the performance of the algorithm in a space of up to 10,000 covariates. Finally the methodology…
Motivated by the genomic application of expression quantitative trait loci (eQTL) mapping, we propose a new procedure to perform simultaneous testing of multiple hypotheses using Bayes factors as input test statistics. One of the most significant features of this method is its robustness in controlling the targeted false discovery rate (FDR) even under misspecifications of parametric alternative models. Moreover, the proposed procedure is highly computationally efficient, which is ideal for treating both complex system and big data in genomic applications. We discuss the theoretical properties…
We consider integrative modeling of multiple gene networks and diverse genomic data, including protein-DNA binding, gene expression and DNA sequence data, to accurately identify the regulatory target genes of a transcription factor (TF). Rather than treating all the genes equally and independently a priori in existing joint modeling approaches, we incorporate the biological prior knowledge that neighboring genes on a gene network tend to be (or not to be) regulated together by a TF. A key contribution of our work is that, to maximize the use of all existing biological knowledge, we allow incor…
Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach -- the Bayesian Ising Approximation (BIA) -- to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regressio…
We consider the problem of statistical inference on unknown quantities structured as a multiway table. We show that such multiway tables are naturally formed by arranging regression coefficients in complex systems of linear models for association analysis. In genetics and genomics, the resulting two-way and three-way tables cover many important applications. Within the Bayesian hierarchical model framework, we define the structure of a multiway table through prior specification. Focusing on model comparison and selection, we derive analytic expressions of Bayes factors and their approximations…
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational inference method using a finite-dimensional Galerkin method. We show that the proposed approximation has a convergence-in-probability property to the solution of the original multi-layered model. We then carry out Bayesian inference using the preconditioned Crank--Nicolson algorithm which is modified to work with multi-layered Gaussian fields. We show via numerica…
Understanding the association between injury severity and patients' potential for recovery is crucial to providing better care for patients with traumatic brain injury (TBI). Estimation of this relationship requires clinical information on injury severity, patient demographics, and healthcare utilization, which are often obtained from separate data sources. Because of privacy and confidentiality regulations, these data sources do not include unique identifiers to link records across data sources. Record linkage is a process to identify records that represent the same entity across data sources…
High-throughput genetic and epigenetic data are often screened for associations with an observed phenotype. For example, one may wish to test hundreds of thousands of genetic variants, or DNA methylation sites, for an association with disease status. These genomic variables can naturally be grouped by the gene they encode, among other criteria. However, standard practice in such applications is independent screening with a universal correction for multiplicity. We propose a Bayesian approach in which the prior probability of an association for a given genomic variable depends on its gene, and …
Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a Gaussian process (GP) to share parameters of the sparsity-inducing prior in proportion to feature similarity as defined by an arbitrary positive definite kernel. For linear regression, this sparsity-inducing prior on regression coefficients is a relaxation of the canonical spike-and-slab prior that flattens the mixture model into a scale mixture of normals. …
In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors. In settings such as genomics, there can be complex interactions among the predictors. By using a carefully-structured Tucker factorization, we define a model that can characterize any conditional probability, while facilitating variable selection and modeling of higher-order interactions. Following a Bayesian approach, we propose a Markov chain Monte Carlo al…
It is well known that the integration among different data-sources is reliable because of its potential of unveiling new functionalities of the genomic expressions which might be dormant in a single source analysis. Moreover, different studies have justified the more powerful analyses of multi-platform data. Toward this, in this study, we consider the circadian genes' omics profile such as copy number changes and RNA sequence data along with their survival response. We develop a Bayesian structural equation modeling coupled with linear regressions and log normal accelerated failure time regres…
The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such …
Acute infection, if not rapidly and accurately detected, can lead to sepsis, organ failure and even death. Current detection of acute infection as well as assessment of a patient's severity of illness are imperfect. Characterization of a patient's immune response by quantifying expression levels of specific genes from blood represents a potentially more timely and precise means of accomplishing both tasks. Machine learning methods provide a platform to leverage this 'host response' for development of deployment-ready classification models. Prioritization of promising classifiers is dependent, …
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for defining distributions on sparsity structure of random eigenmatrices. We explore theoretical aspects and implications for conditional independence structures arising in multivariate Gaussian models, and discuss connections with sparse PCA, factor analysis and Gaussian graphical models. Methodology includes model-based exploratory data analysis and Bayesian analysis…
Integrative analysis of multi-level pharmacogenomic data for modeling dependencies across various biological domains is crucial for developing genomic-testing based treatments. Chain graphs characterize conditional dependence structures of such multi-level data where variables are naturally partitioned into multiple ordered layers, consisting of both directed and undirected edges. Existing literature mostly focus on Gaussian chain graphs, which are ill-suited for non-normal distributions with heavy-tailed marginals, potentially leading to inaccurate inferences. We propose a Bayesian robust cha…
A central part of population genomics consists of finding genomic regions implicated in local adaptation. Population genomic analyses are based on genotyping numerous molecular markers and looking for outlier loci in terms of patterns of genetic differentiation. One of the most common approach for selection scan is based on statistics that measure population differentiation such as $F_{ST}$. However they are important caveats with approaches related to $F_{ST}$ because they require grouping individuals into populations and they additionally assume a particular model of population structure. He…
Significant advances in biotechnology have allowed for simultaneous measurement of molecular data points across multiple genomic and transcriptomic levels from a single tumor/cancer sample. This has motivated systematic approaches to integrate multi-dimensional structured datasets since cancer development and progression is driven by numerous co-ordinated molecular alterations and the interactions between them. We propose a novel two-step Bayesian approach that combines a variable selection framework with integrative structure learning between multiple sources of data. The structure learning i…
Targeted therapies on the basis of genomic aberrations analysis of the tumor have shown promising results in cancer prognosis and treatment. Regardless of tumor type, trials that match patients to targeted therapies for their particular genomic aberrations have become a mainstream direction of therapeutic management of patients with cancer. Therefore, finding the subpopulation of patients who can most benefit from an aberration-specific targeted therapy across multiple cancer types is important. We propose an adaptive Bayesian clinical trial design for patient allocation and subpopulation iden…
In order to identify clusters of objects with features transformed by unknown affine transformations, we develop a Bayesian cluster process which is invariant with respect to certain linear transformations of the feature space and able to cluster data without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant to orthogonal transformations under model I, invariant to scaling-coordinate orthogonal transformations under model II, or invariant to arbitrary non-singular linear transformations under model III. The proposed split-merge algorit…
We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of high-dimensional covariance matrix estimation to multiple cores, solves each subproblem separately via a latent factor model, and then combines these estimates to produce a global estimate of the covariance matrix. Existing divide and conquer methods focus exclusively on dividing the total number of observations $n$ into subsamples while keeping the dimension $p$ fixed.…
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical …
A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs …
Change detection involves segmenting sequential data such that observations in the same segment share some desired properties. Multivariate change detection continues to be a challenging problem due to the variety of ways change points can be correlated across channels and the potentially poor signal-to-noise ratio on individual channels. In this paper, we are interested in locating additive outliers (AO) and level shifts (LS) in the unsupervised setting. We propose ABACUS, Automatic BAyesian Changepoints Under Sparsity, a Bayesian source separation technique to recover latent signals while al…
Network-based analyses of high-throughput genomics data provide a holistic, systems-level understanding of various biological mechanisms for a common population. However, when estimating multiple networks across heterogeneous sub-populations, varying sample sizes pose a challenge in the estimation and inference, as network differences may be driven by differences in power. We are particularly interested in addressing this challenge in the context of proteomic networks for related cancers, as the number of subjects available for rare cancer (sub-)types is often limited. We develop NExUS (Networ…
The discovery of genomic polymorphisms influencing gene expression (also known as expression quantitative trait loci or eQTLs) can be formulated as a sparse Bayesian multivariate/multiple regression problem. An important aspect in the development of such models is the implementation of bespoke inference methodologies, a process which can become quite laborious, when multiple candidate models are being considered. We describe automatic, black-box inference in such models using Stan, a popular probabilistic programming language. The utilisation of systems like Stan can facilitate model prototypi…
Modern cancer genomics datasets involve widely varying sizes and scales, measurement variables, and correlation structures. A fundamental analytical goal in these high-throughput studies is the development of general statistical techniques that can cleanly sift the signal from noise in identifying disease-specific genomic signatures across a set of experimental or biological conditions. We propose BayesDiff, a nonparametric Bayesian approach based on a novel class of first order mixture models, called the Sticky Poisson-Dirichlet process or multicuisine restaurant franchise. The BayesDiff meth…
A number of statistical models have been successfully developed for the analysis of high-throughput data from a single source, but few methods are available for integrating data from different sources. Here we focus on integrating gene expression levels with comparative genomic hybridization (CGH) array measurements collected on the same subjects. We specify a measurement error model that relates the gene expression levels to latent copy number states which, in turn, are related to the observed surrogate CGH measurements via a hidden Markov model. We employ selection priors that exploit the de…
Cambridge Cancer Genomics（剑桥癌症基因组学公司）；The University of Cambridge（剑桥大学）
The genomic profile underlying an individual tumor can be highly informative in the creation of a personalized cancer treatment strategy for a given patient; a practice known as precision oncology. This involves next generation sequencing of a tumor sample and the subsequent identification of genomic aberrations, such as somatic mutations, to provide potential candidates of targeted therapy. The identification of these aberrations from sequencing noise and germline variant background poses a classic classification-style problem. This has been previously broached with many different supervised …
The identification of sets of co-regulated genes that share a common function is a key question of modern genomics. Bayesian profile regression is a semi-supervised mixture modelling approach that makes use of a response to guide inference toward relevant clusterings. Previous applications of profile regression have considered univariate continuous, categorical, and count outcomes. In this work, we extend Bayesian profile regression to cases where the outcome is longitudinal (or multivariate continuous) and provide PReMiuMlongi, an updated version of PReMiuM, the R package for profile regressi…
Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases. However, its practical deployment in genomic data analysis under a Bayesian framework is limited due to both statistical and computational challenges. The statistical challenge is that one needs to infer both the mean vector and the inverse covariance matrix, a problem inherently more complex than separately estimating each. The computational challenge is due to…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been developed for this task, typically based either on universal data compression algorithms, or on statistical estimators of the underlying process distribution. In this work, we propose a fully-Bayesian approach for entropy estimation. Building on the recently introduced Bayesian Context Trees (BCT) framework for modelling discrete time series as variable-memo…
Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and effective SNPs makes the use of sparse modeling of such genetic data sets, highly important. The high-dimensional sparse instrumental variables models are one of such useful association models, which models the simultaneous relation of the gene expressions and genetic variants with complex traits. From a Bayesian viewpoint, the sparsity can be favored using sparsi…
Identifying genetic variants that regulate quantitative traits, or QTLs, is the primary focus of the field of statistical genetics. Most current methods are limited to identifying mean effects, or associations between genotype and the mean value of a quantitative trait. It is possible, however, that a genetic variant may affect the variance of the quantitative trait in lieu of, or in addition to, affecting the trait mean. Here, we develop a general methodological approach to identifying covariates with variance effects on a quantitative trait using a Bayesian heteroskedastic linear regression …
There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in Bayesian nonparametric (BNP) inference for the unseen-features problem: for fixed prior's parameters, they all lead to a Poisson posterior distribution for the number of unseen features, which depends on the sampling information only through the sample size. CRMs are thus not a flexible prior model for the unseen-features problem and, while the Poisson posterior…
The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a smooth approximation via Moreau-Yosida envelopes, and apply gradient-based discretized diffusions to sample from the resulting distribution. We characterize the error of the Moreau-Yosida approximation and propose a novel implementation using underdamped Langevin dynamics. In misson-critical cases, however, replacing the posterior with an approximation may not…
Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates for uncertainty in the resulting integrative models are however unreliable unless inference accounts for the selection of these associations with accuracy. In this article, we develop selection-aware Bayesian methods which: (i) counteract the impact of model selection bias through a "selection-aware posterior" in a flexible class of integrative Bayesian mode…
This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by simulated and real datasets. It can be useful in studies such as clustering, change-point and process control. In order to estimate the mixture weight function, we propose two new Bayesian nonlinear dynamic approaches for polynomial models, that can be extended to other problems involving polynomial nonlinear dynamic models. One of the methods, called here compo…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that only a few entries of two mean vectors or covariance matrices are different. Many existing tests that rely on aggregating the difference between empirical means or covariance matrices are not optimal or yield low power under such setups. Motivated by this, we develop Bayesian two-sample tests employing a divide-and-conquer idea, which is powerful especially wh…
University of Minnesota（明尼苏达大学）；School of Public Health（公共卫生学院）；Division of Biostatistics（生物统计学部）
Distance weighted discrimination (DWD) is a linear discrimination method that is particularly well-suited for classification tasks with high-dimensional data. The DWD coefficients minimize an intuitive objective function, which can solved very efficiently using state-of-the-art optimization techniques. However, DWD has not yet been cast into a model-based framework for statistical inference. In this article we show that DWD identifies the mode of a proper Bayesian posterior distribution, that results from a particular link function for the class probabilities and a shrinkage-inducing proper pr…
This paper presents a new Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler. Contrary to available split-merge procedures, the resulting so-called Particle Gibbs Split-Merge sampler does not require the computation of a complex acceptance ratio, is simple to implement using existing sequential Monte Carlo libraries and can be parallelized. We investigate its performance experimentally on synthetic problems as well as on geolocation and cancer gen…
Learning graphical models from data is an important problem with wide applications, ranging from genomics to the social sciences. Nowadays datasets often have upwards of thousands---sometimes tens or hundreds of thousands---of variables and far fewer samples. To meet this challenge, we have developed a new R package called sparsebn for learning the structure of large, sparse graphical models with a focus on Bayesian networks. While there are many existing software packages for this task, this package focuses on the unique setting of learning large networks from high-dimensional data, possibly …
The emergence of SARS-CoV-2 variants of concern endangers the long-term control of COVID-19, especially in countries with limited genomic surveillance. In this work, we explored genomic drivers of contagion in Chile. We sequenced 3443 SARS-CoV-2 genomes collected between January and July 2021, where the Gamma (P.1), Lambda (C.37), Alpha (B.1.1.7), B.1.1.348, and B.1.1 lineages were predominant. Using a Bayesian model tailored for limited genomic surveillance, we found that Lambda and Gamma variants' reproduction numbers were about 5% and 16% larger than Alpha's, respectively. We observed an ov…
