Schedule for: 23w5030 - Statistical Challenges for Complex Brain Signals and Images

TBA

We present a robust topological method that it will not be affected by subtle changes over time, conditions, and populations. Such a method can be extremely powerful in the presence of large noise, where many existing methods are likely to be producing too much false positives. The robust performance is achieved using the Wasserstein distance on the persistence of topological signals. The probabilistic version of optimal transport is applied in the characterization of epileptic brain network obtained from the resting-state functional magnetic resonance images (rs-fMRI). Our method will not show any confounding effects caused by site and sex. The talk is based on Das et al. 2023 (arXiv:2210.09092).

A central problem in image analysis is to locate where the important effects are spatially. The standard solution has been to treat it as a large-scale multiple testing problem, however this approach assumes signal sparsity and does not provide a measure of spatial uncertainty. We propose to directly address the question of where the important effects are by estimating the excursion set where the signal is greater than a threshold. To assess uncertainty, we construct spatial confidence regions, given as nested sets that spatially bound the true excursion set with a given probability. We develop this approach for excursion sets of the mean function in a signal-plus-noise model, including coefficients in pointwise regression models. We further show that, interestingly, confidence regions with simultaneous control over all excursion thresholds can be obtained by thresholding standard simultaneous confidence bands for functional data. Examples and computational issues are discussed for 3D fMRI data.

Neuroimaging is poised to take a substantial leap forward in understanding the neurophysiological underpinnings of human behavior, due to a combination of improved analytic techniques and the quality of imaging data. These advances are allowing researchers to develop population-level multivariate models of the functional brain representations underlying behavior, performance, clinical status and prognosis, and other outcomes. Population-based models can identify patterns of brain activity, or ‘signatures’, that can predict behavior and decode mental states in new individuals, producing generalizable knowledge and highly reproducible maps. These signatures can capture behavior with large effect sizes and can be used and tested across research groups. However, the potential of such signatures is limited by neuroanatomical constraints, in particular individual variation in functional brain anatomy. To circumvent this problem, current models are either applied only to individual participants, severely limiting generalizability, or force participants’ data into anatomical reference spaces (atlases) that do not respect individual functional topology and boundaries. Here we seek to overcome this shortcoming by developing new topological models for inter-subject alignment, which register participants’ functional brain maps to one another. This increases effective spatial resolution, and more importantly allow us to explicitly analyze the spatial topology of functional maps make inferences on differences in activation location and shape across persons and psychological states. In this talk we discuss several approaches towards functional alignment and highlight promises and pitfalls.

Compared to spatial-extent inference for mean parameters in neuroimaging, statistical methods for testing variance components for heritability and reliability studies are underdeveloped due to methodological and computational challenges. To leverage spatial autocorrelation efficiently, we propose a fast and powerful test called CLEAN-V. It models the global spatial dependence of imaging data, computes locally powerful cluster-enhanced variance component test statistics, and controls FWER using a computationally efficient permutation procedure. We use task-fMRI data from the Human Connectome Project to show the promising performance of CLEAN-V in detecting regions with high heritability and test-retest reliability, which agree with activation regions.

Anomaly detection in random fields is an important problem in many applications including the detection of cracks in concrete. Frequently, such anomalies are visible as areas with different expected values compared to the background noise. For example, in 2D image data of concrete both cracks as well as integral parts of the material constitute areas with different expected values. Due to their different geometric properties we can define scan statistics that enhance cracks and at the same time discard the integral parts of the given concrete. Cracks can then be detected using a suitable threshold for appropriate scan statistics. This is joint work with Philipp Klein (Otto-von-Guericke University Magdeburg) and Marco Meyer (University of Hannover)

Similar to other measures of brain function, functional near-infrared spectroscopy (fNIRS) data take the form of heterogeneous multivariate time series signals. We discuss a novel group-based method for analyzing fNIRS that simultaneously clusters subject-level data into potentially interpretable phenotypes while evaluating associations with clinical and demographic variables. The method models subject-level fNIRS data throughs a mixture of nonparametric time components where mixing weights depends on time-independent exogenous variables and accounts for heterogeneity among subjects. The proposed method is motivated by and illustrated through the analysis of data from a study of infant emotional reactivity and recovery from stress.

The correct estimation of Magnetic Resonance T2 values on tissue helps characterize brain damages such as demyelination, axonal loss, and inflammation. However, because of the low spatial resolution of the MR scans, the contents of a voxel include heterogeneous tissue populations such as grey and white matter, damaged tissues, and cerebrospinal liquid, among others. We present a supervised learning strategy capable of estimating tissue compartments' number and volume (distributions) with different T2 values. The method optimizes the number of MR volumes and then reduces the time the subject needs to be inside the scanner.

We consider assessing the association between brain structural imaging (SI) measures and functional connectome (FC) obtained from neuroimaging data. In this network analysis, the outcomes are off-diagonal elements of an FC (covariance) matrix while predictors are a multivariate vector of SI variables and other covariates. We propose a multilayer network model to capture the systematic association patterns between subsets of SIs and FC sub-networks. The first layer network is a bipartite graph characterizing the association between all SI variables and FC outcomes, where an edge denotes a non-zero SI-FC association. A large proportion of edges are located within latent dense bipartite subgraphs while other edges are randomly and sparsely distributed in the rest of the bipartite graph. The second layer network represents the connectomic graph, where most FC outcomes in the first layer dense subnetworks comprise dense clique subgraphs. The globally sparse and locally dense multilayer network model can reveal which FC subnetworks are systematically influenced by a selected subset of SIs.We develop algorithms to identify the underlying multilayer sub-networks and propose a statistical inference framework to test these sub-networks. We further apply our approach to 4242 participants from UK Biobank to evaluate the effects of whole-brain white matter microstructure integrity and cortical thickness on the whole-brain FC network.

In neuroimaging applications, it becomes increasingly important to study the association between different imaging modalities using image-on-image regression (IIR), which faces many challenges in model interpretations, statistical inferences, and predictions. To address these issues, we propose a new approach: Bayesian Image-on-image Regression via Deep kernel learning based Gaussian Processes (BIRD-GP). Our method consists of two stages of analysis. In Stage 1, we model outcome and predictor images as realizations of GPs and project them respectively on lower-dimensional vector spaces using a kernel expansion approach. We propose a novel DNN-based approach to covariance kernel learning of the GPs providing efficient and accurate image projections. In Stage 2, we specify the associations between the projected outcome images and predictor images using Bayesian DNNs. We develop efficient posterior computation algorithms using the Stein variational gradient descent method. We compare BIRD-GP with the state-of-the-art IIR methods via extensive numerical experiments on synthetic images from the benchmark datasets and analysis of the fMRI data in the Human Connectome Project (HCP).

There is a growing interest in using fMRI data in clinical practice. I present a fully Bayesian model for fMRI that may be more suitable for clinical applications than standard fMRI tools. An order-varying, time-varying autoregressive model is used to capture any non-stationary behavior over time. A data adaptive smoothing CAR model is used to capture any non-stationary behavior over space. Low frequency drift is modeled using adaptive B-spline bases. Priors are placed on the HRF parameters allowing greater modeling flexibility. Therefore, inference is based on a decision theoretic approach that differentially controls false positive and negative rates.

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying structure of the covariance matrix. We evaluate the performance of the proposed approach on a range of simulated datasets and find that it outperforms a range of alternative recently proposed methods. Finally, we use our approach to study changes in the amount of water on the surface of a plot of soil which feeds into model development for degradation of surface piping.

This talk overviews the statistical modeling of correlated count structures, including time series, spatial random fields, and space-time processes. A Gaussian copula is used to produce an extremely flexible count structure that is naturally parsimonious, can have negative autocorrelations, can easily accommodate covariates, and can be statistically fitted by likelihood methods. Some applications of the methods are given.

Stationary points and their latency/amplitude are often critical for a model to be interpretable and may be considered as key features of interest in many applications. Motivated by event-related potentials (ERP) derived from electroencephalography (EEG) signals, we propose a semiparametric Bayesian model to efficiently infer stationary points and characteristic features of a nonparametric function. We use Gaussian processes as a flexible prior for the underlying function and develop fast algorithms for inference. We use simulated data to show how the proposed method automatically identifies characteristic components and their latencies at the individual level, avoiding the excessive averaging across subjects 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.

Eye-tracking (ET) experiments offer a powerful, safe, and feasible platform for gaining insights into attentional processes by providing moment-by-moment gaze patterns to repeated presentation of sensory stimuli (referred to as trials). Even though moment-by-moment gaze patterns are recorded, common analysis through summaries such as total looking time durations in regions of interest, collapse data across trials and trial time. Motivated by two ET tasks from the Autism Biomarkers Consortium for Clinical Trials, we will discuss two novel modeling approaches, aiming to retain information across trial time and trial type.

Speaker 1 - Carla Pinkney, LU. 'Sparse Partial Coherence Estimation for Neuroscience Spike Train Data' $$\\$$ An active area of neuroscience research concerns the characterisation of dependence between neurons as evidenced via their firing patterns and rates. Partial spectral coherence can be used to infer direct interactions between neuronal point processes. To estimate partial coherence, we first require an estimate of the inverse spectral density matrix of the process, which can be a challenging task for high-dimensional data such as spike trains. We introduce a procedure based on the graphical LASSO algorithm for time series data, and obtain estimates of the inverse SDM by optimising an l1-penalised log-likelihood function. This optimisation problem is solved via the alternating direction method of multipliers, and estimates are used to recover the undirected conditional dependence network for a given multivariate point process. $$\\$$ Speaker 2 - Emmanuel Ambriz, CIMAT. 'Estimation of non-simplified bivariate conditional copulas via partial copulas mixtures' $$\\$$ We present a proposal for estimating non-simplified bivariate conditional copulas based on mixtures of partial copulas; a partial copula is the expected conditional copula. The inference of the copulas in the mixture is driven by a clustering procedure of partial copula pseudo-observations, the methodology groups observations that locally present similar dependence structures. Both, the proposed notion of "distance" and the clustering procedure are computationally feasible for high dimensions in the conditioning, so our proposal has the potential to be useful for the construction of multivariate Vine Copula models. $$\\$$ Speaker 3- Anass B. El-Yaagoubi, KAUST 'Spectral Topological Data Analysis for EEG Brain Signals'. $$\\$$ Topological data analysis has become a powerful approach over the last twenty years, mainly because of its ability to capture the shape and the geometry inherent in the data. Specifically, the use of persistence homology for analyzing functional brain connectivity has witnessed considerable success in the literature. It solves the problem of connectivity matrix thresholding at arbitrary levels by considering a filtration of the weighted network across all possible threshold values. Such approaches for analyzing the topological structure of functional brain connectivity rely on simple connectivity measures such as Pearson correlation. To overcome this limitation, we propose a frequency-specific approach that leverages coherence to assess the brain’s functional connectivity, leading to a novel topological summary, the spectral landscape, which is an extension of the persistence landscape. Using this novel approach to analyze the EEG brain connectivity of ADHD subjects, we shed light on the frequency-specific differences in the topology of brain connectivity between healthy controls and ADHD subjects.

Psychophysiological interaction (PPI) models have been largely employed to study task-modulated seed-based brain connectivity in fMRI studies. However, popular implementations of the PPI framework assume that the partial correlation between the seed region and the ROIs is static in the absence of a stimulus, whereas current developments in neuroimaging suggest that functional connectivity is by nature dynamic. In this talk, I present a Bayesian modeling framework that extends the generalized PPI model and estimates task-modulated time-varying background functional connectivity from an fMRI experiment. In order to model the dynamics of the background regression coefficients, the framework employs a time-varying scale-mixture shrinkage prior that enforces sparsity of the non-zero coefficients. The approach can be parallelized to identify functional connectivity patterns for varying choices of the seed region. Then, the significant partial correlations across runs are selected by using a non-marginal decision-theory-based multicomparison framework, which also leads to reduced spurious non-zero PPI effects. The performance of the model is illustrated in a simulation analysis and in an application to data from a serial reaction time experiment.

TBC

Group 1: Israel Martinez Hernandez, John Kornak, Ivor Cribben, Moo K Chung, Rebecca Killick, Timothy Johnson, Emmanuel Ambriz, Luis Ascencio, Hernando Ombao $$ \\ $$ Group 2: Alex Gibberd, Jun Young Park, Claudia Kirch, Jaroslaw Harezlak, Martin Lindquist, Michele Guindani, Anas B. El-Yaagoubi, Shou Chen, Mark Fiecas $$ \\ $$ Group 3: Alonso Ramírez, Amanda Mejia, Jian Kang, Norbert Fortin, Robert Lund, Robert Krafty, Armin Schwartzman, Carla Pinkney, Carolina Euan

We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse (L+S) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the rows of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC.

My talk will be focused on functional time series (FTS). FTS is a sequence of observations observed over time, where each observation is assumed to have characteristics that vary along a continuum, e.g., curves or surfaces. For example, this can be the sequence of fMRIs collected over time. I will describe the different topics I have been working on in functional time series, such as factor models, extreme observations, and trend (detrending) methods.

The 2010 hypothetical ‘Jack’ model attempts to describe the timeline with which different biomarkers change in AD and has sparked much discussion and subsequent research. Understanding this temporal ordering in AD and other forms of dementia has major implications for prediction and clinical trial design. I will present some Bayesian modeling work that aims to estimate the temporal path of brain biomarker changes (imaging and otherwise) in frontotemporal dementia and determine potential differences in trajectories across genetic subtypes. This is collaborative work with UCSF Memory and Aging Center along with the Berry Consultants group.

Factor models and related approaches have seen widespread use in neuroscience to segment activity in fMRI data, however, these often lack explicit modelling of the temporal dynamics. This talk discusses some early studies looking at translating the so-called dynamic factor model (DFM) from econometrics to the fMRI setting, and how the latent VAR model of the DFM can be used to study how neuronal activity propagates. A range of sparse and group-sparse priors are investigated to improve interpretation of the factors, an EM algorithm is constructed to perform inference in such models, and examples on real fMRI data given.

Independent component analysis (ICA) is often applied to functional MRI data to estimate functional topology and connectivity (FC). However, due to low signal-to-noise ratio, subject-level ICA results are typically too noisy to be practically useful. Hierarchical Bayesian ICA models leverage information shared across subjects to improve estimation efficiency. Here, we propose FC template ICA, a hierarchical ICA model using empirical population priors on spatial topology and connectivity. These priors can be derived from large fMRI databases or holdout data. The proposed approach is computationally convenient and validated through simulation studies and data from the Human Connectome Project.

We will have three brainstorming sessions focused on the following tracks: Track 1: Challenges in developing high-dimensional models for brain signals. Track 2: Computational challenges for pre-processing, model implementation, visualization, and software development. Track 3: Machine Learning algorithms and approaches to complement statistical techniques.

There is growing interest in binary-valued brain images from MRI. Binary image data can identify the tissue damaged by a stroke, multiple sclerosis lesions in white matter, or bright spots simply called white matter hyperintensities. We recently proposed a mass univariate approach to modelling crossectional data that addresses the problem of low base rate with a penalised maximum likelihood approach with a probit or logistic model. In this work we consider the additional challenge of longitudinal data. Users often want to interpret results as relative risks instead of odds-ratios, but a log-link with binomial variance function may lead to estimation instabilities when event probabilities are close to 1. To address these issues we use generalized estimating equations with log-link regression structures with identity variance function and unknown dispersion parameter, with a penalty on the GEE of the gradient of the Jeffreys prior to avoid infinite parameter estimates. Our findings from extensive simulation studies show significant improvement over the standard log-link generalized estimating equations by providing finite estimates and achieving convergence when boundary estimates occur. The real data application on UK Biobank brain lesion maps further reveals the instabilities of the standard log-link generalized estimating equations for a large-scale data set and demonstrates the clear interpretation of relative risk in clinical applications.

In this talk, I will present a study of the performance of functional connectivity and dynamic functional connectivity network measures for disease classification of psychiatric disorders. We consider both statistical learning and machine learning classification methods and use various functional magnetic resonance imaging (fMRI) data sets for validation. Time permitting, I will also discuss a new package for brain network visualization and reproducibility in neurostatistics.

Biclustering is the task of simultaneously clustering the samples and features of a dataset. In doing so, subsets of samples that exhibit similar behaviors across subsets of features can be identified. Motivated by a longitudinal diffusion tensor imaging study of sport-related concussion (SRC), we present the problem of biclustering multivariate longitudinal data in which subjects and features are grouped simultaneously based on longitudinal patterns rather than magnitude. We propose a penalized regression-based method for solving this problem by exploiting the heterogeneity in the longitudinal patterns within subjects and features. We evaluate the performance of the proposed methods via a simulation study and perform an analysis of the motivating data set. In this analysis, we reveal subgroups of SRC cases that exhibit heterogeneous patterns of white-matter abnormalities.