Schedule for: 16w5036 - Mathematical and Statistical Challenges in Neuroimaging Data Analysis

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In recent years, there has been significant interest in investigating brain connectivity based on functional neuroimaging data to better understand brain organization and networks. A wide range of network modeling tools has been proposed for this goal. The simplest and most commonly used methods, such as full correlation, measure the marginal connection between fMRI time-series from a pair of brain regions. Some other methods, such as partial correlation, aim to measure the direct connectivity between brain regions by adjusting for the effects from other regions. Several important questions relevant to network analysis include: how does the brain network change when we construct the network based on direct connection as against marginal connection; how does the brain network change when we apply different levels of sparse regularization in estimating the network; whether and how functional connections are related to structural connections in the brain network. In this talk, we discuss methods and analyses that we have recently worked on in the effort to search for answers to these questions. We will present some interesting findings in our exploration of brain connectivity based on resting-state fMRI and diffusion MRI.

In this talk, we consider the challenge in modeling time-evolving effective connectivity, the dynamic changes in causal interactions between many different brain regions. Effective connectivity is traditionally assumed constant and modeled using stationary vector autoregressive (VAR) models. However, recent studies which focused on the undirected dynamic connectivity using sliding-window analysis or time-varying (TV) coefficient models fail to capture simultaneously both slow and abrupt changes. We present a unified framework for reliable and adaptive estimation of state-related changes in effective connectivity, based on switching VAR (SVAR) models. Under this model, the dynamic connectivity regimes are uniquely characterized by distinct high dimensional VAR processes, which switch between a finite number of underlying quasistationary brain states. The evolution of states and the associated directed dependencies are defined by a Markov chain and the SVAR parameters. Our algorithm has three stages: (Stage 1.) Feature extraction using TV-VAR coefficients which we estimate with different types of penalties; (Stage 2.) Preliminary regime identification, via clustering of the TV-VAR coefficients; (Stage 3.) Following the initial estimates from the first two stages, refined regime segmentation is accomplished by Kalman smoothing and SVAR parameter estimation via the expectation-maximization (EM) algorithm under a state-space formulation. Simulation results show accurate regime change detection and connectivity estimates by the SVAR approach. When applied to real motor-task fMRI and epileptic seizure EEG data, the proposed method was able to identify statedependent directed connectivity changes via the switching of the VAR states. This is in collaboration with Yuxiao Wang (UC Irvine) and Chee-Ming Ting (Univ Teknologi Malaysia)

Motivated by the needs of selecting important features from big neuroimaging data, we develop a new Bayesian feature screening approach in the generalized linear model (GLM) framework. We assign the conjugate priors on the coefficients and obtain the analytical form of the marginal posterior density function. Under some mild regularity conditions, we show that the marginal posterior moments follow a mixture of normal distributions. In light of this theoretical foundation, we develop a Bayesian variable screening algorithm for ultra-high dimensional data consisting of two steps: Step 1: compute a multivariate variable screening statistic based on marginal posterior moments; Step 2: perform the mixture model-based cluster analysis on screening statistics to identify the unimportant variables. Step 1 only requires a computational complexity on the linear order of the number of predictors and it is straightforward to be parallelized. It has a close connection with sure independent screening (SIS) statistics and high-dimensional ordinary least-squares projection (HOLP) methods. Step 2 is an extension of the local false discovery rate (FDR) analysis. We implement our method using massively parallel computing techniques based on the general-purpose computing on graphics processing units (GPGPU), leading to an ultra-fast variable screening procedure. Our simulation studies show that the proposed approach can perform variable screening on one million predictors within seconds and achieve higher selection accuracy compared with existing methods. We also illustrate our methods on an analysis of resting state functional magnetic resonance imaging (Rs-fMRI) data from the Autism Brain Imaging Data Exchange (ABIDE) study.

In many human brain network studies, we do not have sufficient number (n) of images relative to the number (p) of voxels due to the prohibitively expensive cost of scanning enough subjects. Thus, brain network models usually suffer the small-n large-p problem. Such a problem is often remedied by sparse network models, which are usually solved numerically by optimizing L1-penalties. Unfortunately, due to the computational bottleneck associated with optimizing L1-penalties, it is not practical to apply such methods to learn large-scale brain networks. In this paper, we introduce a new sparse network model based on cross-correlations that bypass the computational bottleneck. Our model can build sparse brain networks at the voxel level with p > 25000. Instead of using a single sparse parameter that may not be optimal in other studies and datasets, the computational speed gain enables us to analyze the collection of networks at every possible sparse parameter in a coherent mathematical framework via persistent homology. The method is subsequently applied in determining the extent of heritability on functional brain networks at the voxel-level for the first time using twin fMRI. This is a joint work with Paul Rathouz of University of Wisconsin-Madison, David Zald of Vanderbilt University and Benjamin Lahey of University of Chicago.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. Please don't be late, or you will not be in the official group photo! The photograph will be taken outdoors so a jacket might be required.

Noise is a common issue for all Magnetic Resonance Imaging (MRI) techniques and obviously leads to variability of the estimates in any model describing the data. A number of special MR sequences as well as increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from its theoretical value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasi-likelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate that the problem is relevant even for data from the Human Connectome Project, one of the highest quality diffusion MRI data available so far.

There is growing evidence that individual differences among depression patients on Electrophysiology (EEG), fMRI and other brain imaging measurements may be predictive of potential treatment response. In this talk we discuss approaches to identifying potential placebo responders, i.e., a subgroup who benefits sufficiently from inactive drug treatments, using EEG measurements as a matrix (order-2 tensor) predictor. Given the high dimensionality of the problem, we consider a reduced rank regression model with a data-driven regularization. Our approach will be evaluated through simulations and will be applied to data from a large placebo-controlled clinical trial of major depressive disorders.

In functional magnetic resonance imaging, images of the brain are acquired as rapidly as physically possible to cover the necessary brain, but also capture cognitive temporal dynamics. Although the standard gradient echo-echo planar k-space acquisition is relatively fast, when aggregated over many slices, it takes a relatively long time to obtain a single volume image. The reason for the appreciable amount of time for each image is the finite amount of time it takes to measure k-space data. Techniques to accelerate the image acquisition process have made much progress by measuring less k-space data and performing image reconstruction via an estimation of missing data using other image information. This talk will review the measurement and reconstruction of fully-sampled and sub-sampled k-space data in addition to their resulting statistical properties.

I will survey the range of quantitative metrics used in the literature for evaluating the performance of functional neuroimaging processing pipelines and attempt to compare their strengths and weaknesses. Metrics to be discussed will include: ROC and Pseudo-ROC Curves, Cluster Overlap Metrics, Intra-class Correlation Coefficients and extensions, Spatial Pattern Reproducibility, Similarity Metric Ranking Approaches, Cross-validated Prediction, and Combinations of Metrics. In particular I will focus on interactions between data preprocessing/cleaning and data analysis, and whether it makes sense to treat these as separate independent choices when evaluating pipelines.

There is significant interest in understanding how structural/functional connectivity changes in the brain explain behavioral symptoms in neurodegenerative diseases such as Alzheimer’s disease (AD). Clear variations in connectivity at the dementia stage of the disease have been identified in the literature. Despite such findings, AD-related connectivity changes in the preclinical stage of the disease still remain poorly characterized. Such preclinical datasets are typically smaller in size and group differences are subtle, making analysis challenging. This talk will describe some of our recent efforts to overcome these difficulties in an effort to elucidate how brain connectivity varies as a function of genotype and various other risk factors, even in asymptomatic individuals. The engine driving these analyses is a new multi-resolution scheme for performing statistical analysis of connectivity networks derived from neuroimaging data. Our algorithm derives a wavelet representation at each connection edge which captures the graph context at multiple resolutions. Extensive empirical evidence shows how this framework offers improved statistical power in analyzing structural connectivity in diffusion tensor images (DTI) obtained via so-called tractography methods. We will present results showing connectivity differences between AD patients and controls that were not evident using standard approaches. Later, we will show results on individuals that are not yet diagnosed with AD but have a positive family history risk of AD where our algorithm helps in identifying potentially subtle differences between patient groups. An open source toolbox implementing this framework has been made available. Joint work with Nagesh Adluru, Emily Balczewski, Barb Bendlin, Moo Chung, SeongJae Hwang, Sterling Johnson, WonHwa Kim and Ozioma Okonkwo.

Diffusion magnetic resonance imaging (D-MRI) is an imaging technology which uses water diffusion as a proxy to probe the anatomy of biological tissues in an in-vivo and non-invasive way. D-MRI has been widely used to reconstruct white matter fiber tracts and to provide information on structure connectivity of the brain. In D-MRI, fiber orientation distribution (FOD) function is a spherical p.d.f. that characterizes the fiber distribution at each voxel of the brain white matter. The observed diffusion weighted measurements at the corresponding voxel can be modeled as spherical convolution between FOD and a response function. We will discuss the estimation of FOD based on a spherical needlets representation. The needlets are localized both in frequency and space and form a tight frame on the space of square integrable spherical functions. Needlets representation of FOD is sparse as FOD is a smooth function with a few sharp peaks (each corresponding to a major fiber bundle). We will derive the needlets representation of FOD by an l1 penalized regression with non-negativity constraints. Comparing with existing methods based on spherical harmonics representation, the proposed method leads to much better peak localization, particularly when the separation angles among fiber bundles are small. Joint work with Hao Yan from UC Davis.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Advances in technology for brain imaging and genotyping have motivated studies examining the relationships between genetic variation and brain structure. Wang et al. (Bioinformatics, 2012) developed an approach for simultaneous regression parameter estimation and SNP selection based on penalized regression with a group l_{2,1}-norm penalty. The group-norm penalty formulation incorporates the biological group structures among SNPs induced from their genetic arrangement and enforces sparsity at the group level. Wang et al. do not provide standard errors or other inferential methodology for their parameter estimates. In this paper, we propose a corresponding Bayesian model that allows for full posterior inference for the regression parameters using Gibbs sampling. Properties of our method are investigated using simulation studies and the methodology is applied to a large dataset collected as part of the Alzheimer's Disease Neuroimaging Initiative.

Imaging genetics has rapidly emerged as a promising approach for investigating the genetic determinants of brain mechanisms that underlie an individual's behavior or psychiatric condition. By combining single-nucleotide polymorphism (SNP) arrays and functional magnetic resonance imaging (fMRI), we propose an integrative Bayesian risk prediction model that allows us to discriminate between individuals with schizophrenia and healthy controls, based on a sparse set of discriminatory regions of interest (ROIs) and SNPs. Inference on a regulatory network between SNPs and ROI intensities (ROI-SNP network) is used in a single modeling framework to inform the selection of the discriminatory ROIs and SNPs. We use simulation studies to assess the performance of our method and apply it to data collected from individuals with schizophrenia and healthy controls. We found our approach to outperform competing methods that do not link the ROI-SNP network to the selection of discriminatory markers.

The major computing cost for estimating the voxel-wise brain connectivity, especially the precision matrix, is from the tuning parameter selection. Recently we established the convergence rates for thresholding estimation of large covariance matrix and graphic-lasso estimation of large precision matrix for temporally correlated data with temporal correlations bounded by certain polynomial decay rate that can be long-memory. We found that the estimating convergence rates only depend on the temporal correlation decay rate via sample size – the number of images measured over time, which is fixed for a given data set, whereas their relations to the dimension of each image are (almost) independent of the temporal correlation decay rate. This observation motivates us to consider a tuning parameter selection procedure using cross-validation via low dimensional submatrices. Simulation results and a voxel-wise resting state fMRI data analysis will be presented.

Functional connectivity (FC) - the study of the statistical association between time series from anatomically distinct regions - has become one of the primary areas of research in the field surrounding resting state functional magnetic resonance imaging (rs-fMRI). While, for many years researchers have implicitly assumed that FC was stationary across time in rs-fMRI, it has recently become increasingly clear that this is not the case and the ability to assess dynamic changes in FC is critical for better understanding of the inner workings of the human brain. Currently, the most common strategy for estimating these dynamic changes is by using the sliding window technique. However, its greatest shortcoming is the inherent variation present in the estimate, even for null data, which is easily confused with true time-varying changes in connectivity. This can have serious consequences as even spurious fluctuations caused by noise can easily be confused with the signal of interest. For these reasons, assessment of uncertainty in the sliding window correlation estimates is of critical importance. Here we propose a new approach that combines the multivariate linear process bootstrap (MLPB) method and sliding-window techniques, to assess the uncertainty in dynamic FC estimates by providing its confidence bands. Both numerical results and an application to fMRI study are presented showing the efficacy of the proposed method. Joint work with Maria Kudela and Martin Lindquist.

In a typical diffusion tensor Imaging (DTI) study, diffusion properties are observed among multiple fiber bundles to understand the association between neurodevelopment and clinical variables, such as age, gender, biomarkers, etc. Most research focuses on individual tracts or use summary statistics to jointly study a group of tracts, which usually ignores the global and individual functional structures. To address this problem, we propose a hierarchical functional principal regression model, consisting of three components: (i) a multidimensional Gaussian process model to characterize functional data, (ii) a latent factor model to jointly analyze multiple fiber bundles and to capture common effect shared among tracts, and (iii) a multivariate regression model study tract-specific effect. A multilevel estimation procedure is proposed and a global statistic is introduced to test hypothesis of interest. Simulation is conducted to evaluate the performance of HPRM in estimating shared effect and individual effect. We also applied HPRM to a genome-wide association study (Gwas) of one-year twins to explore important genetic markers in brain development among young children.

The connection structure in an individual’s brain plays a fundamental role in how the mind responds to everyday tasks and life’s challenges. Modern imaging technology such as diffusion MRI (dMRI) makes it easy to peer into an individual’s brain and collect valuable data to infer the structural connectivity. The difficulty for current statistical analysis of such data is to extract precise and robust connectivity networks from the brain. In this talk, we are presenting a state-of-the-art data processing pipeline to reliably construct structural connectivity from dMRI, including streamline extraction, adaptive streamline compression, and robust connectivity matrix construction. I will also discuss some potential statistical analyses to the extracted data.

Relative perihematomal edema volume (edema volume divided by hematoma volume) has been reported to be a potential predictor of functional outcome in patients with hyperacute spontaneous Intracerebral Hemorrhage (ICH). The hematoma edema segmentation on Computed Tomography (CT) is very challenging due to substantial overlapping between the edema and surrounding brain tissues, and also image noise. An automatic segmentation algorithm is presented. The algorithm first applies a threshold value based approach to segment the hematoma in each 2D slice. And then the edema segmentation part applies a non-local fuzzy c-means clustering algorithm on the 3D region of interest (ROI) volume by combing the selected 2D hematoma area acquired in the first step. The proposed algorithm has been applied to the CT head images of 4 patients with ICH, and it provides reliable and reproducible segmentations that are similar to the manual segmentation of physicians. This is joint work with Dr. Linglong Kong, Dr. Rohana Karunamuni, Dr. Ken Butcher, Lili Zheng and Rebecca McCourt.

Twin studies can be used to disentangle the environmental and genetic contributions to brain structure and function. A trait's heritability can be estimated using Fisher's Additive, Common, and unique Environmental (ACE) model, which can be formulated as a structural equation model (SEM). The Human Connectome Project has generated large amounts of preprocessed imaging data from twin pairs. A massive univariate analysis would estimate an SEM at each location in the brain. An important question is whether the genetic contribution is significant over a region-of-interest. Extending the ACE model to spatial domains requires an estimation of the covariance functions. Here we propose a spatial functional SEM. We develop a method for large covariance estimation using functional PCA. Our framework allows for inference over arbitrary domains of the cortex. Additionally, the approach improves predictions. Joint work with Dr. Hongtu Zhu

The hurdle to neuroimaging analysis for many statisticians is learning how to process neuroimaging data. As this data can be in specific formats for neuroimaging, it may not even be clear how to read the data into a software package. As many statisticians use R for statistical analysis, one goal is to have neuroimaging preprocessing in the same language. Many of these functions for neuroimaging processing are available in software suites with differing syntax and functionality. We present the R package fslr that ports these neuroimaging functions from the popular and open-source FSL software, such as brain segmentation, Gaussian smoothing, image registration, and tissue-class segmentation. We will discuss the advantages of having this package within R, as well as other packages being developed that allow for a full suite of neuroimaging tools for statisticians who use R.

More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing millions of genome-wide associations with functional signals sampled at millions of locations in the brain from thousands of subjects. In this talk, we are presenting a Fast Functional Genome Wide Association Study (FFGWAS) framework to carry out whole-genome analyses of multimodal imaging data. FFGWAS consists of three components including (1) a multivariate varying coefficient model for modeling the relation between multiple functional imaging responses and a set of covariates (both genetic and non-genetic predictors), (2) a global sure independence screening (GSIS) procedure for reducing the dimension from a very large scale to a moderate scale, and (3) a detection procedure for detect significant cluster-locus pairs. We also successfully applied FFGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 30,000 vertices on hippocampal surface, and 501,584 SNPs.

Topics: Grant opportunity, Grant review criterion for BRAIN, Neuroconduct, Software development in R or matlab, and Train next-generation statisticians.

Network connectivity is often intimately linked with measures of covariance and correlation. However, it is not always clear as to how to best handle such covariances in fMRI data, as they are often in reality more complex than simple correlations between time series. In this work, we will examine a few different approaches which arise from taking a functional data analysis approach to the problem. We will investigate time changing connectivity via functional change point detection and also spatially constrained connectivity, based on the use of penalised functional principal components.

In this talk, I will describe a set of spatial functional regression modeling strategies for modeling event-related potential data. These strategies attempt to flexibly account for their complex spatio-temporal structure while relating the ERPs to covariates while providing rigorous multiplicity-adjusted inference and scaling up to large studies. Various model comparison measures are introduced and described to assess which models best fit the data, and the methods are applied to a smoking cessation study to assess neurological response to different types of visual stimuli. These methods are also applicable to other types of neuroimaging data.

In many cancer imaging settings, radiologists identify the presence of solid tumors through informal assessment of the extent to which candidate regions of interest absorb and maintain contrast over a series of a few repeated scans. Often multiple interdependent ROIs are evaluated in isolation, using data from only a few scans. Independent estimation appears limiting for analysis of sparse functional data derived from dynamic imaging techniques that use physiological models to derive multiple interdependent biomarkers acquired from multiple regions of interests (ROI) within the same organ. We consider statistical methods for joint estimation of sparse spatiotemporally correlated imaging-biomarkers using semi-parametric models. Joint prediction is used to identify liver metastases using perfusion characteristics from multiple ROIs acquired using dynamic computed tomography.

Tissue perfusion plays a critical role in oncology. Cancerous cell growth and migration requires the proliferation of networks of new blood vessels through the process of angiogenesis, triggering modifications to the vasculature of surrounding host tissue. Measurements from perfusion imaging modalities provide physiological correlates for neovascularization induced by tumor angiogenesis. Such measurements are often generated repeatedly over time and at multiple spatially interdependent units. To reduce model complexity and simplify the resulting inference, possible spatial correlation among neighboring units is often neglected. I will talk about a weighted kernel smoothing estimate of the mean function that leverages the spatial and temporal correlation, particularly, in the presence of sparse observations. The companion problem of developing a simultaneous prediction method for individual curves using discrete samples will also be discussed.

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependences that are often encoded in terms of partial correlations. Such a graph is inferred from neuroimaging data such as electroencephalography and functional magnetic resonance imaging. In this talk, we discuss a number of projects addressing estimation and inference of brain connectivity network through partial correlation matrix.

Many challenges remain for group-level whole-brain connectivity network analyses because the massive connectomics connectivity metrics are correlated and the correlation structure is constrained by the extraordinarily complex, yet highly organized, topology of the underlying neural architecture. To detect the truly differentially expressed brain connectivity, for example, between subjects with mental disorders and healthy controls using the high dimensional omics data often face with the tradeoff between false positive discoveries and the lack of power. We consider that the differentially expressed connectivity metrics/edges are not randomly distributed in the whole-brain connectivity structure but rather in an organized topological structure. We develop several novel machine learning algorithms to automatically detect topological structures, and furthermore .

Quantile regression with functional response and scalar covariates has become an important statistical tool for many neuroimaging studies. In this paper, we study optimal estimation of varying coefficient functions in the framework of reproducing kernel Hilbert space. Minimax rates of convergence under both fixed and random designs are established. We have developed easily implementable estimators which are shown to be rate-optimal. Simulations and real data analysis are conducted to examine the finite-sample performance. This is a joint work with Linglong Kong, Zhengwu Zhang, and Hongtu Zhu.

The aim of this effort is to develop a spatial Gaussian predictive process (SGPP) framework for accurately predicting neuroimaging data by using a set of covariates of interest, such as age and diagnostic status, and an existing neuroimaging data set. To achieve better prediction, we not only delineate spatial association between neuroimaging data and covariates, but also explicitly model spatial dependence in neuroimaging data. The SGPP model uses a functional principal component model to capture medium-to-long-range (or global) spatial dependence, while SGPP uses a multivariate simultaneous autoregressive model to capture short-range (or local) spatial dependence as well as cross-correlations of different imaging modalities. We propose a three-stage estimation procedure to simultaneously estimate varying regression coefficients across voxels and the global and local spatial dependence structures. Furthermore, we develop a predictive method to use the spatial correlations as well as the cross-correlations by employing a cokriging technique, which can be useful for the imputation of missing imaging data. Simulation studies and real data analysis are used to evaluate the prediction accuracy of SGPP and show that SGPP significantly outperforms several competing methods, such as voxel-wise linear model, in prediction. Although we focus on the morphometric variation of lateral ventricle surfaces in a clinical study of neurodevelopment, it is expected that SGPP is applicable to other imaging modalities and features.

We present a Bayesian nonparametric regression model for the analysis of multiple-subject functional magnetic resonance imaging (fMRI) data. Our goal is to provide a joint analytical framework that allows the detection of regions of the brain that activate in response to a stimulus, while simultaneously taking into account the association, or clustering, of spatially remote voxels within and across subjects. The model incorporates information on both the spatial and temporal correlation structures of the data. It also allows for voxel-dependent and subject-specific parameters. The high dimensionality of the data and the large amount of parameters to be estimated pose computational challenges. We employ variational Bayes algorithms as an approximate computational technique and compare efficiency and estimation results with respect to a full Monte Carlo Markov chain algorithm. We explore performances of the proposed model on simulated data and on real fMRI data.

A major goal of precision medicine is to use information gathered at the time that a patient presents for treatment to help clinicians determine, separately for each patient the particular treatment that provides the best-expected outcome. In psychiatry it is thought that various brain imaging techniques may allow for the discovery of information vital to predicting response to treatment. We will present the general problem of using both scalar and functional data to guide patient-specific treatment decisions and describe some approaches that can be used to perform model fitting and variable selection. Joint work with Adam Ciarleglio, Eva Petkova, and Thaddeus Tarpey.

A variety of anatomical structures in human brain can be represented as functions (curves or surfaces) on intervals or spheres. Examples of curves include DTI fiber tracts and sulcal folds while examples of surfaces include subcortical structures (hippocampus, thalamus, putamen, etc). Morphological analysis and statistical modeling of such data faces the following challenges: the representation spaces are curved, the data is seldom registered, the classical Hilbert structure is problematic, and (nowdays) there is a tremendous amount of data to deal with. Many current methods handle these challenges as pre-processing, using off the shelf software, resulting in sub-optimal solutions. Elastic FDA provides a unified framework for dealing with nonlinear geometries and simultaneous registration of function data, and leads to efficient computer algorithms. It has proven to outperform all recent methods in registering functional data. The FPCA, resulting from linearized representations under elastic Riemannian metrics, has been used for solving regression and testing under appropriate models. I will present some recent extensions of this work involving morphological analysis of tree-like structures such as neurons.

Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of methods development ashighlighted by Varoquaux and Craddock (2013) that ``there is currently no unique solution, but a spectrum of related methods and analytical strategies" to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters.The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data. Joint work with Junghi Kim.

We propose statistical methods for quantifying variability in a population of connectomes using general representations. While the graphical model literature is growing, little work has been done comprehensively studying populations of graphs in without distributional assumptions. To study this, we use generalized variances for complex objects based on distance statistics. We further develop methods for two-sample testing at the whole connectome and the subnetwork levels and study the asymptotic properties of the test statistics. We demonstrate the utility of these methods in a connectomic study of autism spectrum disorders using diffusion tensor imaging.

We use ordinary differential equations (ODEs) to model the human brain as a continuous-time dynamic system whose components, i.e. brain regions, biophysically interact with each other. In contrast to existing ODE models that focus on directional connectivity among only a few brain regions, we propose a widely applicable high-dimensional ODE model to explore connectivity among multiple small brain regions. The new model, called the modular and indicator-based dynamic directional model (MIDDM), uses indicators to represent significant directional interactions among brain regions and features a cluster structure, which consists of modules of densely connected brain regions. We develop a Bayesian hierarchical model to make inferences about the MIDDM and also to provide a new statistical approach to quantifying ODE model uncertainty that arises from the inherent inadequacy of the ODE model for a complex system. Specifically, we represent the state functions of the MIDDM by spline bases, assign a prior dependent on the MIDDM to basis coefficients, impose the Potts-model prior on cluster structures, and use a deliberately designed scaled ``spike-and-slab'' type of prior for indicators in the MIDDM. The ensuing joint posterior distribution for basis coefficients and the MIDDM parameters has well defined posterior conditional distributions, from which we use a partially collapsed Gibbs Sampler to draw posterior samples. To further speed up the posterior simulation, we employ parallel computing schemes in two Markov Chain Monte Carlo steps. An easy-to-implement hyperparameter selection strategy has also been developed. We apply the proposed Bayesian framework to an auditory electrocorticography dataset to identify significant clusters and directional effects among different brain regions.

To date, most functional Magnetic Resonance Imaging (fMRI) studies have assumed that the functional connectivity (FC) between time series from distinct brain regions is constant across time. However, recently, there has been increased interest in quantifying possible dynamic changes in FC during fMRI experiments, as it is thought this may provide insight into the fundamental workings of brain networks. In this talk we discuss statistical methods for assessing dynamic FC, recent findings, and future directions in this emerging research area.

Topological data analysis (TDA) has been popularized since its development in early 2000. TDA has shown its effectiveness in discerning true features from noise in high-dimensional data. In this talk, we will introduce persistent homology, a particular branch of computational topology and discuss how it can be incorporated to classical statistics and techniques in machine learning. We will demonstrate its usefulness in classifying ADHD subjects. This is a joint project with Rui Hu, Zhichun Zhai, Linglong Kong and Bei Jiang.

I will present a new framework for discriminative anatomy detection in high dimensional neuroimaging data. Current methods for identifying significant regions related to a group study typically use voxel-based mass univariate approaches. Those methods have limited ability to identify complex population differences because they do not take into account multivariate relationships in data. High dimensional pattern classification methods aim to optimally perform feature extraction and selection to find a set of features that differentiate the groups. However, they do not directly produce anatomically interpretable features. Following recent advances in sparse dimensionality reduction methods, we propose a sparse classification method that identifies anatomical regions that are both discriminative and clinically interpretable. Results on synthetic and real MRI data of multiple sclerosis patients and age- and gender-matched healthy controls show superior performance of our method in detecting stable and significant regions in a statistical group analysis when compared to a generative sparse method and to a voxel-based analysis method.

Neuroimaging data are very high dimensional and complicated. A human scientist cannot apprehend the raw data directly. One primary purpose of neuroimaging data analysis is to abstract away most of the dimensionality and complexity in the data by extracting just a small number of significant patterns from it. This analysis involves a long chain of steps that interact with the data at various points. Ideally, each step would "just work", yielding reliable outputs robust to noise and complexity in the data. In practice, the analysis can fail at various steps due to a host of reasons such as the influence of noise, bad convergence in some optimization algorithm, and so on. However, the final output of the analysis often provides no indication that such failures have occurred. By design, the analysis abstracts away the complexity of both the data and how the data interacts with the analysis itself. The analysis ends up hiding such failures, so it is necessary to look for them deliberately. Another important consideration is that the analysis often abstracts away too much of the structure in the neuroimaging data. Meaningful patterns go undetected. I will discuss several approaches for delving into what the data analysis is doing to allow for improved robustness through quality assurance checking as well as improved interpretation through consideration of important patterns in the data that often go unnoticed.

The conventional estimates of functional connectivity do not account for temporal autocorrelation or heterogeneity across subjects in an experiment; the former leads to inflated Type I errors in a single-subject analysis and the latter leads to low power in a group analysis. To address this, we propose a flexible general linear model framework for estimating functional connectivity that accounts for 1) temporal autocorrelation and 2) heterogeneity across subjects by allowing for subject-specific estimates of the variance. We compare the performance of our model to other methods using an extensive simulation study. We also apply the new model to a resting-state functional magnetic resonance imaging (fMRI) study to compare the functional connectivity networks jointly in both typical and reading-impaired young adults in order to characterize the resting state networks that are related to reading processes.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.