arXiv subjects

Marina Vannucci

Publications and source records attributed to Marina Vannucci.

At least 37 records · Page 2Linked to original sources

arXiv2023

Bayesian Tensor Modeling for Image-based Classification of Alzheimer's Disease

Tensor-based representations are being increasingly used to represent complex data types such as imaging data, due to their appealing properties such as dimension reduction and the preservation of spatial information. Recently, there is a growing literature on using Bayesian scalar-on-tensor regression techniques that use tensor-based representations for high-dimensional and spatially distributed covariates to predict continuous outcomes. However surprisingly, there is limited development on corresponding Bayesian classification methods relying on tensor-valued covariates. Standard approaches that vectorize the image are not desirable due to the loss of spatial structure, and alternate methods that use extracted features from the image in the predictive model may suffer from information loss. We propose a novel data augmentation-based Bayesian classification approach relying on tensor-valued covariates, with a focus on imaging predictors. We propose two data augmentation schemes, one resulting in a support vector machine (SVM) classifier, and another yielding a logistic regression classifier. While both types of classifiers have been proposed independently in literature, our contribution is to extend such existing methodology to accommodate high-dimensional tensor valued predictors that involve low rank decompositions of the coefficient matrix while preserving the spatial information in the image. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for implementing these methods. Simulation studies show significant improvements in classification accuracy and parameter estimation compared to routinely used classification methods. We further illustrate our method in a neuroimaging application using cortical thickness MRI data from Alzheimer's Disease Neuroimaging Initiative, with results displaying better classification accuracy throughout several classification tasks.

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arXiv2023

Semiparametric Latent ANOVA Model for Event-Related Potentials

Event-related potentials (ERPs) extracted from electroencephalography (EEG) data in response to stimuli are widely used in psychological and neuroscience experiments. A major goal is to link ERP characteristic components to subject-level covariates. Existing methods typically follow two-step approaches, first identifying ERP components using peak detection methods and then relating them to the covariates. This approach, however, can lead to loss of efficiency due to inaccurate estimates in the initial step, especially considering the low signal-to-noise ratio of EEG data. To address this challenge, we propose a semiparametric latent ANOVA model (SLAM) that unifies inference on ERP components and their association to covariates. SLAM models ERP waveforms via a structured Gaussian process prior that encodes ERP latency in its derivative and links the subject-level latencies to covariates using a latent ANOVA. This unified Bayesian framework provides estimation at both population- and subject- levels, improving the efficiency of the inference by leveraging information across subjects. We automate posterior inference and hyperparameter tuning using a Monte Carlo expectation-maximization algorithm. We demonstrate the advantages of SLAM over competing methods via simulations. Our method allows us to examine how factors or covariates affect the magnitude and/or latency of ERP components, which in turn reflect cognitive, psychological or neural processes. We exemplify this via an application to data from an ERP experiment on speech recognition, where we assess the effect of age on two components of interest. Our results verify the scientific findings that older people take a longer reaction time to respond to external stimuli because of the delay in perception and brain processes.

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arXiv2023

Semiparametric Bayesian Inference for Local Extrema of Functions in the Presence of Noise

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of noise. By viewing the function as an infinite-dimensional nuisance parameter, a semiparametric formulation of this problem poses daunting challenges, both methodologically and theoretically, as (i) the number of local extrema may be unknown, and (ii) the induced shape constraints associated with local extrema are highly irregular. In this article, we build upon a derivative-constrained Gaussian process prior recently proposed by Yu et al. (2023) to derive what we call an encompassing approach that indexes possibly multiple local extrema by a single parameter. We provide closed-form characterization of the posterior distribution and study its large sample behavior under this unconventional encompassing regime. We show that the posterior measure converges to a mixture of Gaussians with the number of components matching the underlying truth, leading to posterior exploration that accounts for multi-modality. Point and interval estimates of local extrema with frequentist properties are also provided. The encompassing approach leads to a remarkably simple, fast semiparametric approach for inference on local extrema. We illustrate the method through simulations and a real data application to event-related potential analysis.

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arXiv2023

A Bayesian Joint Model for Compositional Mediation Effect Selection in Microbiome Data

Analyzing multivariate count data generated by high-throughput sequencing technology in microbiome research studies is challenging due to the high-dimensional and compositional structure of the data and overdispersion. In practice, researchers are often interested in investigating how the microbiome may mediate the relation between an assigned treatment and an observed phenotypic response. Existing approaches designed for compositional mediation analysis are unable to simultaneously determine the presence of direct effects, relative indirect effects, and overall indirect effects, while quantifying their uncertainty. We propose a formulation of a Bayesian joint model for compositional data that allows for the identification, estimation, and uncertainty quantification of various causal estimands in high-dimensional mediation analysis. We conduct simulation studies and compare our method's mediation effects selection performance with existing methods. Finally, we apply our method to a benchmark data set investigating the sub-therapeutic antibiotic treatment effect on body weight in early-life mice.

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arXiv2023

A Predictor-Informed Multi-Subject Bayesian Approach for Dynamic Functional Connectivity

Time Varying Functional Connectivity (TVFC) investigates how the interactions among brain regions vary over the course of an fMRI experiment. The transitions between different individual connectivity states can be modulated by changes in underlying physiological mechanisms that drive functional network dynamics, e.g., changes in attention or cognitive effort as measured by pupil dilation. In this paper, we develop a multi-subject Bayesian framework for estimating dynamic functional networks as a function of time-varying exogenous physiological covariates that are simultaneously recorded in each subject during the fMRI experiment. More specifically, we consider a dynamic Gaussian graphical model approach, where a non-homogeneous hidden Markov model is employed to classify the fMRI time series into latent neurological states, borrowing strength over the entire time course of the experiment. The state-transition probabilities are assumed to vary over time and across subjects, as a function of the underlying covariates, allowing for the estimation of recurrent connectivity patterns and the sharing of networks among the subjects. Our modeling approach further assumes sparsity in the network structures, via shrinkage priors. We achieve edge selection in the estimated graph structures, by introducing a multi-comparison procedure for shrinkage-based inferences with Bayesian false discovery rate control. We apply our modeling framework on a resting-state experiment where fMRI data have been collected concurrently with pupillometry measurements, leading us to assess the heterogeneity of the effects of changes in pupil dilation, previously linked to changes in norepinephrine-containing locus coeruleus, on the subjects' propensity to change connectivity states.

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arXiv2022

Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that extends a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e, at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing `participation rate' parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, the proposed model construction is the first in the Bayesian literature to simultaneously achieve image smoothing, parameter estimation and a two-level variable selection for image-on-scalar regression.

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arXiv2022

Bayesian Non-Homogeneous Hidden Markov Model with Variable Selection for Investigating Drivers of Seizure Risk Cycling

A major issue in the clinical management of epilepsy is the unpredictability of seizures. Yet, traditional approaches to seizure forecasting and risk assessment in epilepsy rely heavily on raw seizure frequencies, which are a stochastic measurement of seizure risk. We consider a Bayesian non-homogeneous hidden Markov model for unsupervised clustering of zero-inflated seizure count data. The proposed model allows for a probabilistic estimate of the sequence of seizure risk states at the individual level. It also offers significant improvement over prior approaches by incorporating a variable selection prior for the identification of clinical covariates that drive seizure risk changes and accommodating highly granular data. For inference, we implement an efficient sampler that employs stochastic search and data augmentation techniques. We evaluate model performance on simulated seizure count data. We then demonstrate the clinical utility of the proposed model by analyzing daily seizure count data from 133 patients with Dravet syndrome collected through the Seizure Tracker TM system, a patient-reported electronic seizure diary. We report on the dynamics of seizure risk cycling, including validation of several known pharmacologic relationships. We also uncover novel findings characterizing the presence and volatility of risk states in Dravet syndrome, which may directly inform counseling to reduce the unpredictability of seizures for patients with this devastating cause of epilepsy.

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arXiv2021

Bayesian Inference for Stationary Points in Gaussian Process Regression Models for Event-Related Potentials Analysis

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the locations of stationary points of a nonparametric function, while treating the function itself as a nuisance parameter. We use Gaussian processes as a flexible prior for the underlying function and impose derivative constraints to control the function's shape via conditioning. We develop an inferential strategy that intentionally restricts estimation to the case of at least one stationary point, bypassing possible mis-specifications in the number of stationary points and avoiding the varying dimension problem that often brings in computational complexity. We illustrate the proposed methods using simulations and then apply the method to the estimation of event-related potentials (ERP) derived from electroencephalography (EEG) signals. We show how the proposed method automatically identifies characteristic components and their latencies at the individual level, which avoids the excessive averaging across subjects which is routinely done in the field to obtain smooth curves. By applying this approach to EEG data collected from younger and older adults during a speech perception task, we are able to demonstrate how the time course of speech perception processes changes with age.

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arXiv2021

A Bayesian model of microbiome data for simultaneous identification of covariate associations and prediction of phenotypic outcomes

One of the major research questions regarding human microbiome studies is the feasibility of designing interventions that modulate the composition of the microbiome to promote health and cure disease. This requires extensive understanding of the modulating factors of the microbiome, such as dietary intake, as well as the relation between microbial composition and phenotypic outcomes, such as body mass index (BMI). Previous efforts have modeled these data separately, employing two-step approaches that can produce biased interpretations of the results. Here, we propose a Bayesian joint model that simultaneously identifies clinical covariates associated with microbial composition data and predicts a phenotypic response using information contained in the compositional data. Using spike-and-slab priors, our approach can handle high-dimensional compositional as well as clinical data. Additionally, we accommodate the compositional structure of the data via balances and overdispersion typically found in microbial samples. We apply our model to understand the relations between dietary intake, microbial samples, and BMI. In this analysis, we find numerous associations between microbial taxa and dietary factors that may lead to a microbiome that is generally more hospitable to the development of chronic diseases, such as obesity. Additionally, we demonstrate on simulated data how our method outperforms two-step approaches and also present a sensitivity analysis.

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arXiv2021

Latent Network Estimation and Variable Selection for Compositional Data via Variational EM

Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to simultaneously estimate network interactions and associations to relevant covariates for count data, and specifically for compositional data, which have a fixed sum constraint. We use a hierarchical Bayesian model with latent layers and employ spike-and-slab priors for both edge and covariate selection. For posterior inference, we develop a novel variational inference scheme with an expectation maximization step, to enable efficient estimation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of network recovery. We show the practical utility of our model via an application to microbiome data. The human microbiome has been shown to contribute to many of the functions of the human body, and also to be linked with a number of diseases. In our application, we seek to better understand the interaction between microbes and relevant covariates, as well as the interaction of microbes with each other. We provide a Python implementation of our algorithm, called SINC (Simultaneous Inference for Networks and Covariates), available online.

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arXiv2021

Evidence of state-dependence in the effectiveness of responsive neurostimulation for seizure modulation

An implanted device for brain-responsive neurostimulation (RNS System) is approved as an effective treatment to reduce seizures in adults with medically-refractory focal epilepsy. Clinical trials of the RNS System demonstrate population-level reduction in average seizure frequency, but therapeutic response is highly variable. Recent evidence links seizures to cyclical fluctuations in underlying risk. We tested the hypothesis that effectiveness of responsive neurostimulation varies based on current state within cyclical risk fluctuations. We analyzed retrospective data from 25 adults with medically-refractory focal epilepsy implanted with the RNS System. Chronic electrocorticography was used to record electrographic seizures, and hidden Markov models decoded seizures into fluctuations in underlying risk. State-dependent associations of RNS System stimulation parameters with changes in risk were estimated. Higher charge density was associated with improved outcomes, both for remaining in a low seizure risk state and for transitioning from a high to a low seizure risk state. The effect of stimulation frequency depended on initial seizure risk state: when starting in a low risk state, higher stimulation frequencies were associated with remaining in a low risk state, but when starting in a high risk state, lower stimulation frequencies were associated with transition to a low risk state. Findings were consistent across bipolar and monopolar stimulation configurations. The impact of RNS on seizure frequency exhibits state-dependence, such that stimulation parameters which are effective in one seizure risk state may not be effective in another. These findings represent conceptual advances in understanding the therapeutic mechanism of RNS, and directly inform current practices of RNS tuning and the development of next-generation neurostimulation systems.

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arXiv2020

A Bayesian Time-Varying Effect Model for Behavioral mHealth Data

The integration of mobile health (mHealth) devices into behavioral health research has fundamentally changed the way researchers and interventionalists are able to collect data as well as deploy and evaluate intervention strategies. In these studies, researchers often collect intensive longitudinal data (ILD) using ecological momentary assessment methods, which aim to capture psychological, emotional, and environmental factors that may relate to a behavioral outcome in near real-time. In order to investigate ILD collected in a novel, smartphone-based smoking cessation study, we propose a Bayesian variable selection approach for time-varying effect models, designed to identify dynamic relations between potential risk factors and smoking behaviors in the critical moments around a quit attempt. We use parameter-expansion and data-augmentation techniques to efficiently explore how the underlying structure of these relations varies over time and across subjects. We achieve deeper insights into these relations by introducing nonparametric priors for regression coefficients that cluster similar effects for risk factors while simultaneously determining their inclusion. Results indicate that our approach is well-positioned to help researchers effectively evaluate, design, and deliver tailored intervention strategies in the critical moments surrounding a quit attempt.

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arXiv2020

BVAR-Connect: A Variational Bayes Approach to Multi-Subject Vector Autoregressive Models for Inference on Brain Connectivity Networks

In this paper we propose BVAR-connect, a variational inference approach to a Bayesian multi-subject vector autoregressive (VAR) model for inference on effective brain connectivity based on resting-state functional MRI data. The modeling framework uses a Bayesian variable selection approach that flexibly integrates multi-modal data, in particular structural diffusion tensor imaging (DTI) data, into the prior construction. The variational inference approach we develop allows scalability of the methods and results in the ability to estimate subject- and group-level brain connectivity networks over whole-brain parcellations of the data. We provide a brief description of a user-friendly MATLAB GUI released for public use. We assess performance on simulated data, where we show that the proposed inference method can achieve comparable accuracy to the sampling-based Markov Chain Monte Carlo approach but at a much lower computational cost. We also address the case of subject groups with imbalanced sample sizes. Finally, we illustrate the methods on resting-state functional MRI and structural DTI data on children with a history of traumatic injury.

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arXiv2020

Bayesian Modeling of Multiple Structural Connectivity Networks During the Progression of Alzheimer's Disease

Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of participants who were either healthy control, or with mild cognitive impairment, or Alzheimer's disease patients. For this purpose, we develop a novel approach for inference of multiple networks with related edge values across groups. Specifically, we infer a Gaussian graphical model for each group within a joint framework, where we rely on Bayesian hierarchical priors to link the precision matrix entries across groups. Our proposal differs from existing approaches in that it flexibly learns which groups have the most similar edge values, and accounts for the strength of connection (rather than only edge presence or absence) when sharing information across groups. Our results identify key alterations in structural connectivity which may reflect disruptions to the healthy brain, such as decreased connectivity within the occipital lobe with increasing disease severity. We also illustrate the proposed method through simulations, where we demonstrate its performance in structure learning and precision matrix estimation with respect to alternative approaches.

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arXiv2019

Bayesian Inference of Networks Across Multiple Sample Groups and Data Types

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of Chronic Obstructive Pulmonary Disease (COPD).

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arXiv2014

A hierarchical Bayesian model for inference of copy number variants and their association to gene expression

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 dependencies across adjacent copy number states and investigate MCMC stochastic search techniques for posterior inference. Our approach results in a unified modeling framework for simultaneously inferring copy number variants (CNV) and identifying their significant associations with mRNA transcripts abundance. We show performance on simulated data and illustrate an application to data from a genomic study on human cancer cell lines.

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arXiv2012

Regularized Partial Least Squares with an Application to NMR Spectroscopy

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexibility, general penalties, easy interpretation of results, and fast computation in high-dimensional settings. We also outline extensions of our methods leading to novel methods for Non-negative PLS and Generalized PLS, an adaption of PLS for structured data. We demonstrate the utility of our methods through simulations and a case study on proton Nuclear Magnetic Resonance (NMR) spectroscopy data.

stat.ML↗

arXiv2011

Incorporating biological information into linear models: A Bayesian approach to the selection of pathways and genes

The vast amount of biological knowledge accumulated over the years has allowed researchers to identify various biochemical interactions and define different families of pathways. There is an increased interest in identifying pathways and pathway elements involved in particular biological processes. Drug discovery efforts, for example, are focused on identifying biomarkers as well as pathways related to a disease. We propose a Bayesian model that addresses this question by incorporating information on pathways and gene networks in the analysis of DNA microarray data. Such information is used to define pathway summaries, specify prior distributions, and structure the MCMC moves to fit the model. We illustrate the method with an application to gene expression data with censored survival outcomes. In addition to identifying markers that would have been missed otherwise and improving prediction accuracy, the integration of existing biological knowledge into the analysis provides a better understanding of underlying molecular processes.

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