arXiv subjects

Martin A. Lindquist

Publications and source records attributed to Martin A. Lindquist.

At least 19 recordsLinked to original sources

arXiv2026

Functional Moments Regression

The Gaussian Process (GP) assumption is often used in functional data analysis. We propose a method to assess departures from the GP assumption, both in terms of the shape of the distribution and its potential dependence on covariates, using a sequence of functional moment regressions. Our methods are inspired by and applied to objectively measured minute-level physical activity data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 study. In this setting, we find that the GP assumption is not satisfied, quantify the associations between functional moments and covariates, and show that standard data transformations, such as the log transformation, do not resolve the discrepancy between assumptions and reality. We further show that when the effect sizes are moderate, inference on the functional fixed effects is largely unaffected by departures from the GP assumption. However, when effect sizes are small, both inference and prediction of subject-level data can be strongly affected. Extensive simulations support these findings. This pragmatic paper presents new methods for real data analysis, with implications for statistical methodology and for understanding human activity and health.

stat.ME↗

arXiv2026

Statistical Opportunities in Neuroimaging

Neuroimaging has profoundly enhanced our understanding of the human brain by characterizing its structure, function, and connectivity through modalities like MRI, fMRI, EEG, and PET. These technologies have enabled major breakthroughs across the lifespan, from early brain development to neurodegenerative and neuropsychiatric disorders. Despite these advances, the brain is a complex, multiscale system, and neuroimaging measurements are correspondingly high-dimensional. This creates major statistical challenges, including measurement noise, motion-related artifacts, substantial inter-subject and site/scanner variability, and the sheer scale of modern studies. This paper explores statistical opportunities and challenges in neuroimaging across four key areas: (i) brain development from birth to age 20, (ii) the adult and aging brain, (iii) neurodegeneration and neuropsychiatric disorders, and (iv) brain encoding and decoding. After a quick tutorial on major imaging technologies, we review cutting-edge studies, underscore data and modeling challenges, and highlight research opportunities for statisticians. We conclude by emphasizing that close collaboration among statisticians, neuroscientists, and clinicians is essential for translating neuroimaging advances into improved diagnostics, deeper mechanistic insight, and more personalized treatments.

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arXiv2025

BrainMT: A Hybrid Mamba-Transformer Architecture for Modeling Long-Range Dependencies in Functional MRI Data

Recent advances in deep learning have made it possible to predict phenotypic measures directly from functional magnetic resonance imaging (fMRI) brain volumes, sparking significant interest in the neuroimaging community. However, existing approaches, primarily based on convolutional neural networks or transformer architectures, often struggle to model the complex relationships inherent in fMRI data, limited by their inability to capture long-range spatial and temporal dependencies. To overcome these shortcomings, we introduce BrainMT, a novel hybrid framework designed to efficiently learn and integrate long-range spatiotemporal attributes in fMRI data. Our framework operates in two stages: (1) a bidirectional Mamba block with a temporal-first scanning mechanism to capture global temporal interactions in a computationally efficient manner; and (2) a transformer block leveraging self-attention to model global spatial relationships across the deep features processed by the Mamba block. Extensive experiments on two large-scale public datasets, UKBioBank and the Human Connectome Project, demonstrate that BrainMT achieves state-of-the-art performance on both classification (sex prediction) and regression (cognitive intelligence prediction) tasks, outperforming existing methods by a significant margin. Our code and implementation details will be made publicly available at this https://github.com/arunkumar-kannan/BrainMT-fMRI

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arXiv2024

Detection of Multiple Influential Observations on Model Selection

Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified through influential diagnostics, which aim to capture observations that unduly bias model estimation. To date, methods for identifying observations that influence the selection of a stochastically chosen submodel have been underdeveloped, especially in the high-dimensional setting where the number of predictors $p$ exceeds the sample size $n$. Recently we proposed an improved diagnostic measure to handle this setting. However, its distributional properties and approximations have not yet been explored. To address this shortcoming, we revisit the notion of exchangeability to determine the exact asymptotic distribution of our assessment measure. This foundation enables the introduction of theoretically supported parametric and nonparametric approaches for distributional approximation and derivation of thresholds for outlier identification. The resulting framework is further extended to logistic regression models and evaluated by comprehensive simulation studies comparing the performance of various detection methods. Finally, the framework is applied to data from a task-based fMRI study of thermal pain, with the goal of identifying outliers that distort the formulation of the statistical model using functional brain activity to predict physical pain ratings. Both linear and logistic models are used to demonstrate the benefits of detection and compare the performance of different detection procedures. In particular, we identify two influential observations that were not detected in prior studies

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arXiv2024

Assessing Influential Observations in Pain Prediction using fMRI Data

Neuroimaging data allows researchers to model the relationship between multivariate patterns of brain activity and outcomes related to mental states and behaviors. However, the existence of outlying participants can potentially undermine the generalizability of these models and jeopardize the validity of downstream statistical analysis. To date, the ability to detect and account for participants unduly influencing various model selection approaches have been sorely lacking. Motivated by a task-based functional magnetic resonance imaging (fMRI) study of thermal pain, we propose and establish the asymptotic distribution for a diagnostic measure applicable to a number of different model selectors. A high-dimensional clustering procedure is further combined with this measure to detect multiple influential observations. In a series of simulations, our proposed method demonstrates clear advantages over existing methods in terms of improved detection performance, leading to enhanced predictive and variable selection outcomes. Application of our method to data from the thermal pain study illustrates the influence of outlying participants, in particular with regards to differences in activation between low and intense pain conditions. This allows for the selection of an interpretable model with high prediction power after removal of the detected observations. Though inspired by the fMRI-based thermal pain study, our methods are broadly applicable to other high-dimensional data types.

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arXiv2023

A tensor based varying-coefficient model for multi-modal neuroimaging data analysis

All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time neuroimaging data is increasingly being combined with other non-imaging modalities, such as behavioral and genetic data. The data structure of many of these modalities can be expressed as time-varying multidimensional arrays (tensors), collected at different time-points on multiple subjects. Here, we consider a new approach for the study of neural correlates in the presence of tensor-valued brain images and tensor-valued predictors, where both data types are collected over the same set of time points. We propose a time-varying tensor regression model with an inherent structural composition of responses and covariates. Regression coefficients are expressed using the B-spline technique, and the basis function coefficients are estimated using CP-decomposition by minimizing a penalized loss function. We develop a varying-coefficient model for the tensor-valued regression model, where both predictors and responses are modeled as tensors. This development is a non-trivial extension of function-on-function concurrent linear models for complex and large structural data where the inherent structures are preserved. In addition to the methodological and theoretical development, the efficacy of the proposed method based on both simulated and real data analysis (e.g., the combination of eye-tracking data and functional magnetic resonance imaging (fMRI) data) is also discussed.

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arXiv2022

Improved fMRI-based Pain Prediction using Bayesian Group-wise Functional Registration

In recent years, neuroimaging has undergone a paradigm shift, moving away from the traditional brain mapping approach toward developing integrated, multivariate brain models that can predict categories of mental events. However, large interindividual differences in brain anatomy and functional localization after standard anatomical alignment remain a major limitation in performing this analysis, as it leads to feature misalignment across subjects in subsequent predictive models.

stat.AP↗

arXiv2022

Mode decomposition-based time-varying phase synchronization for fMRI Data

Recently there has been significant interest in measuring time-varying functional connectivity (TVC) between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. However, this requires the \textit{a priori} choice of type and cut-off frequencies for the bandpass filter needed to perform the analysis. Here we explore alternative approaches based on the use of various mode decomposition (MD) techniques that circumvent this issue. These techniques allow for the data driven decomposition of signals jointly into narrow-band components at different frequencies, thus fulfilling the requirements needed to measure PS. We explore several variants of MD, including empirical mode decomposition (EMD), bivariate EMD (BEMD), noise-assisted multivariate EMD (na-MEMD), and introduce the use of multivariate variational mode decomposition (MVMD) in the context of estimating time-varying PS. We contrast the approaches using a series of simulations and application to rs-fMRI data. Our results show that MVMD outperforms other evaluated MD approaches, and further suggests that this approach can be used as a tool to reliably investigate time-varying PS in rs-fMRI data.

eess.SP↗

arXiv2021

Bayesian Functional Registration of fMRI Activation Maps

Functional magnetic resonance imaging (fMRI) has provided invaluable insight into our understanding of human behavior. However, large inter-individual differences in both brain anatomy and functional localization after anatomical alignment remain a major limitation in conducting group analyses and performing population-level inference. This paper addresses this problem by developing and validating a new computational technique for reducing misalignment across individuals in functional brain systems by spatially transforming each subject's functional data to a common reference map. Our proposed Bayesian functional registration approach allows us to assess differences in brain function across subjects and individual differences in activation topology. It combines intensity-based and feature-based information into an integrated framework and allows inference to be performed on the transformation via the posterior samples. We evaluate the method in a simulation study and apply it to data from a study of thermal pain. We find that the proposed approach provides increased sensitivity for group-level inference.

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arXiv2020

Evaluating phase synchronization methods in fMRI: a comparison study and new approaches

In recent years there has been growing interest in measuring time-varying functional connectivity between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. There are several ways to perform such analyses, and here we compare methods that utilize a PS metric together with a sliding window, referred to here as windowed phase synchronization (WPS), with those that directly measure the instantaneous phase synchronization (IPS). In particular, IPS has recently gained popularity as it offers single time-point resolution of time-resolved fMRI connectivity. In this paper, we discuss the underlying assumptions required for performing PS analyses and emphasize the necessity of band-pass filtering the data to obtain valid results. We review various methods for evaluating PS and introduce a new approach within the IPS framework denoted the cosine of the relative phase (CRP). We contrast methods through a series of simulations and application to rs-fMRI data. Our results indicate that CRP outperforms other tested methods and overcomes issues related to undetected temporal transitions from positive to negative associations common in IPS analysis. Further, in contrast to phase coherence, CRP unfolds the distribution of PS measures, which benefits subsequent clustering of PS matrices into recurring brain states.

eess.SP↗

arXiv2018

Automatic Identification of Twin Zygosity in Resting-State Functional MRI

A key strength of twin studies arises from the fact that there are two types of twins, monozygotic and dizygotic, that share differing amounts of genetic information. Accurate differentiation of twin types allows efficient inference on genetic influences in a population. However, identification of zygosity is often prone to errors without genotying. In this study, we propose a novel pairwise feature representation to classify the zygosity of twin pairs of resting state functional magnetic resonance images (rs-fMRI). For this, we project an fMRI signal to a set of basis functions and use the projection coefficients as the compact and discriminative feature representation of noisy fMRI. We encode the relationship between twins as the correlation between the new feature representations across brain regions. We employ hill climbing variable selection to identify brain regions that are the most genetically affected. The proposed framework was applied to 208 twin pairs and achieved 94.19% classification accuracy in automatically identifying the zygosity of paired images.

eess.IV↗

arXiv2018

Sparse Principal Component based High-Dimensional Mediation Analysis

Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. With multiple mediators, which are potentially causally dependent, the possible decomposition of pathway effects grows exponentially with the number of mediators. Huang and Pan (2016) introduced a principal component analysis (PCA) based approach to address this challenge, in which the transformed mediators are conditionally independent given the orthogonality of the PCs. However, the transformed mediator PCs, which are linear combinations of original mediators, are difficult to interpret. In this study, we propose a sparse high-dimensional mediation analysis approach by adopting the sparse PCA method introduced by Zou and others (2006) to the mediation setting. We apply the approach to a task-based functional magnetic resonance imaging study, and show that our proposed method is able to detect biologically meaningful results related to the identified mediator.

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arXiv2017

A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in Bayesian spatial models. However, as no Bayesian spatial model has been proposed for cs-fMRI data, most analyses continue to employ the classical, voxel-wise general linear model (GLM) (Worsley and Friston 1995). Here, we propose a Bayesian GLM for cs-fMRI, which employs a class of sophisticated spatial processes to flexibly model latent activation fields. We use integrated nested Laplacian approximation (INLA), a highly accurate and efficient Bayesian computation technique (Rue et al. 2009). To identify regions of activation, we propose an excursions set method based on the joint posterior distribution of the latent fields, which eliminates the need for multiple comparisons correction. Finally, we address a gap in the existing literature by proposing a novel Bayesian approach for multi-subject analysis. The methods are validated and compared to the classical GLM through simulation studies and a motor task fMRI study from the Human Connectome Project. The proposed Bayesian approach results in smoother activation estimates, more accurate false positive control, and increased power to detect truly active regions.

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arXiv2017

A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explanatory variables in both the mean and variance (e.g., time trends, activation stimuli, head motion parameters and their temporal derivatives), and to compute the posterior probability of inclusion from the MCMC output. Variable selection is also applied to the lags in the autoregressive noise process, making it possible to infer the lag order from the data simultaneously with all other model parameters. We use both simulated data and real fMRI data from OpenfMRI to illustrate the importance of proper modeling of heteroscedasticity in fMRI data analysis. Our results show that the GLMH tends to detect more brain activity, compared to its homoscedastic counterpart, by allowing the variance to change over time depending on the degree of head motion.

stat.AP↗

arXiv2016

PCA leverage: outlier detection for high-dimensional functional magnetic resonance imaging data

Outlier detection for high-dimensional (HD) data is a popular topic in modern statistical research. However, one source of HD data that has received relatively little attention is functional magnetic resonance images (fMRI), which consists of hundreds of thousands of measurements sampled at hundreds of time points. At a time when the availability of fMRI data is rapidly growing---primarily through large, publicly available grassroots datasets---automated quality control and outlier detection methods are greatly needed. We propose PCA leverage and demonstrate how it can be used to identify outlying time points in an fMRI run. Furthermore, PCA leverage is a measure of the influence of each observation on the estimation of principal components, which are often of interest in fMRI data. We also propose an alternative measure, PCA robust distance, which is less sensitive to outliers and has controllable statistical properties. The proposed methods are validated through simulation studies and are shown to be highly accurate. We also conduct a reliability study using resting-state fMRI data from the Autism Brain Imaging Data Exchange and find that removal of outliers using the proposed methods results in more reliable estimation of subject-level resting-state networks using ICA.

stat.ME↗

arXiv2016

High-dimensional Multivariate Mediation: with Application to Neuroimaging Data

Mediation analysis has become an important tool in the behavioral sciences for investigating the role of intermediate variables that lie in the path between a randomized treatment and an outcome variable. The influence of the intermediate variable on the outcome is often explored using structural equation models (SEMs), with model coefficients interpreted as possible effects. While there has been significant research on the topic in recent years, little work has been done on mediation analysis when the intermediate variable (mediator) is a high-dimensional vector. In this work we present a new method for exploratory mediation analysis in this setting called the directions of mediation (DMs). The first DM is defined as the linear combination of the elements of a high-dimensional vector of potential mediators that maximizes the likelihood of the SEM. The subsequent DMs are defined as linear combinations of the elements of the high-dimensional vector that are orthonormal to the previous DMs and maximize the likelihood of the SEM. We provide an estimation algorithm and establish the asymptotic properties of the obtained estimators. This method is well suited for cases when many potential mediators are measured. Examples of high-dimensional potential mediators are brain images composed of hundreds of thousands of voxels, genetic variation measured at millions of SNPs, or vectors of thousands of variables in large-scale epidemiological studies. We demonstrate the method using a functional magnetic resonance imaging (fMRI) study of thermal pain where we are interested in determining which brain locations mediate the relationship between the application of a thermal stimulus and self-reported pain.

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arXiv2016

Effects of Scan Length and Shrinkage on Reliability of Resting-State Functional Connectivity in the Human Connectome Project

In this paper, we use data from the Human Connectome Project (N=461) to investigate the effect of scan length on reliability of resting-state functional connectivity (rsFC) estimates produced from resting-state functional magnetic resonance imaging (rsfMRI). Additionally, we study the benefits of empirical Bayes shrinkage, in which subject-level estimates borrow strength from the population average by trading a small increase in bias for a greater reduction in variance. For each subject, we compute raw and shrinkage estimates of rsFC between 300 regions identified through independent components analysis (ICA) based on rsfMRI scans varying from 3 to 30 minutes in length. The time course for each region is determined using dual regression, and rsFC is estimated as the Pearson correlation between each pair of time courses. Shrinkage estimates for each subject are computed as a weighted average between the raw subject-level estimate and the population average estimate, where the weight is determined for each connection by the relationship of within-subject variance to between-subject variance. We find that shrinkage estimates exhibit greater reliability than raw estimates for most connections, with 30-40% improvement using scans less than 10 minutes in length and 10-20% improvement using scans of 20-30 minutes. We also observe significant spatial variability in reliability of both raw and shrinkage estimates, with connections within the default mode and motor networks exhibiting the greatest reliability and between-network connections exhibiting the poorest reliability. We conclude that the scan length required for reliable estimation of rsFC depends on the specific connections of interest, and shrinkage can be used to increase reliability of rsFC, even when produced from long, high-quality rsfMRI scans.

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arXiv2015

Improving Reliability of Subject-Level Resting-State fMRI Parcellation with Shrinkage Estimators

A recent interest in resting state functional magnetic resonance imaging (rsfMRI) lies in subdividing the human brain into anatomically and functionally distinct regions of interest. For example, brain parcellation is often used for defining the network nodes in connectivity studies. While inference has traditionally been performed on group-level data, there is a growing interest in parcellating single subject data. However, this is difficult due to the low signal-to-noise ratio of rsfMRI data, combined with typically short scan lengths. A large number of brain parcellation approaches employ clustering, which begins with a measure of similarity or distance between voxels. The goal of this work is to improve the reproducibility of single-subject parcellation using shrinkage estimators of such measures, allowing the noisy subject-specific estimator to "borrow strength" in a principled manner from a larger population of subjects. We present several empirical Bayes shrinkage estimators and outline methods for shrinkage when multiple scans are not available for each subject. We perform shrinkage on raw intervoxel correlation estimates and use both raw and shrinkage estimates to produce parcellations by performing clustering on the voxels. Our proposed method is agnostic to the choice of clustering method and can be used as a pre-processing step for any clustering algorithm. Using two datasets---a simulated dataset where the true parcellation is known and is subject-specific and a test-retest dataset consisting of two 7-minute rsfMRI scans from 20 subjects---we show that parcellations produced from shrinkage correlation estimates have higher reliability and validity than those produced from raw estimates. Application to test-retest data shows that using shrinkage estimators increases the reproducibility of subject-specific parcellations of the motor cortex by up to 30%.

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