Search

Uncertainty quantification of deep neural networks has become an active field of research and plays a crucial role in various downstream tasks such as active learning. Recent advances in evidential deep learning shed light on the direct quantification of aleatoric and epistemic uncertainties with a single forward pass of the model. Most traditional approaches adopt an entropy-based method to derive evidential uncertainty in classification, quantifying uncertainty at the sample level. However, the variance-based method that has been widely applied in regression problems is seldom used in the classification setting. In this work, we adapt the variance-based approach from regression to classification, quantifying classification uncertainty at the class level. The variance decomposition technique in regression is extended to class covariance decomposition in classification based on the law of total covariance, and the class correlation is also derived from the covariance. Experiments on cross-domain datasets are conducted to illustrate that the variance-based approach not only results in similar accuracy as the entropy-based one in active domain adaptation but also brings information about class-wise uncertainties as well as between-class correlations. The code is available at https://github.com/KerryDRX/EvidentialADA. This alternative means of evidential uncertainty quantification will give researchers more options when class uncertainties and correlations are important in their applications., Comment: IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) 2024

Massive Open Online Courses (MOOCs) have transformed the educational landscape, offering scalable and flexible learning opportunities, particularly in data-centric fields like data science and artificial intelligence. Incorporating AI and data science into MOOCs is a potential means of enhancing the learning experience through adaptive learning approaches. In this context, we introduce PyGlide, a proof-of-concept open-source MOOC delivery system that underscores autonomy, transparency, and collaboration in maintaining course content. We provide a user-friendly, step-by-step guide for PyGlide, emphasizing its distinct advantage of not requiring any local software installation for students. Highlighting its potential to enhance accessibility, inclusivity, and the manageability of course materials, we showcase PyGlide's practical application in a continuous integration pipeline on GitHub. We believe that PyGlide charts a promising course for the future of open-source MOOCs, effectively addressing crucial challenges in online education.

Purpose: The aim of this work is to develop a neural network training framework for continual training of small amounts of medical imaging data and create heuristics to assess training in the absence of a hold-out validation or test set. Materials and Methods: We formulated a retrospective sequential learning approach that would train and consistently update a model on mini-batches of medical images over time. We address problems that impede sequential learning such as overfitting, catastrophic forgetting, and concept drift through PyTorch convolutional neural networks (CNN) and publicly available Medical MNIST and NIH Chest X-Ray imaging datasets. We begin by comparing two methods for a sequentially trained CNN with and without base pre-training. We then transition to two methods of unique training and validation data recruitment to estimate full information extraction without overfitting. Lastly, we consider an example of real-life data that shows how our approach would see mainstream research implementation. Results: For the first experiment, both approaches successfully reach a ~95% accuracy threshold, although the short pre-training step enables sequential accuracy to plateau in fewer steps. The second experiment comparing two methods showed better performance with the second method which crosses the ~90% accuracy threshold much sooner. The final experiment showed a slight advantage with a pre-training step that allows the CNN to cross ~60% threshold much sooner than without pre-training. Conclusion: We have displayed sequential learning as a serviceable multi-classification technique statistically comparable to traditional CNNs that can acquire data in small increments feasible for clinically realistic scenarios.

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.

In this study, a density-on-density regression model is introduced, where the association between densities is elucidated via a warping function. The proposed model has the advantage of a being straightforward demonstration of how one density transforms into another. Using the Riemannian representation of density functions, which is the square-root function (or half density), the model is defined in the correspondingly constructed Riemannian manifold. To estimate the warping function, it is proposed to minimize the average Hellinger distance, which is equivalent to minimizing the average Fisher-Rao distance between densities. An optimization algorithm is introduced by estimating the smooth monotone transformation of the warping function. Asymptotic properties of the proposed estimator are discussed. Simulation studies demonstrate the superior performance of the proposed approach over competing approaches in predicting outcome density functions. Applying to a proteomic-imaging study from the Alzheimer's Disease Neuroimaging Initiative, the proposed approach illustrates the connection between the distribution of protein abundance in the cerebrospinal fluid and the distribution of brain regional volume. Discrepancies among cognitive normal subjects, patients with mild cognitive impairment, and Alzheimer's disease (AD) are identified and the findings are in line with existing knowledge about AD.

In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a scalar outcome via a regression model. We propose a direct regression for such distribution-valued covariates that circumvents estimating subject-specific densities and directly uses the observed repeated measures as covariates. The model is invariant to any transformation or ordering of the repeated measures. Endowing the regression function with a Gaussian Process prior, we obtain closed form or conjugate Bayesian inference. Our method subsumes the standard Bayesian non-parametric regression using Gaussian Processes as a special case. Theoretically, we show that the method can achieve an optimal estimation error bound. To our knowledge, this is the first theoretical study on Bayesian regression using distribution-valued covariates. Through simulation studies and analysis of activity count dataset, we demonstrate that our method performs better than approaches that require an intermediate density estimation step.

Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded performance improvements beyond narrow applications and translated to expanded multitask models capable of generalizing across multiple data types and modalities. Simultaneously, it has been shown that neural networks are overparameterized to a high degree, and pruning techniques have proved capable of significantly reducing the number of active weights within the network while largely preserving performance. In this work, we identify a methodology and network representational structure which allows a pruned network to employ previously unused weights to learn subsequent tasks. We employ these methodologies on well-known benchmarking datasets for testing purposes and show that networks trained using our approaches are able to learn multiple tasks, which may be related or unrelated, in parallel or in sequence without sacrificing performance on any task or exhibiting catastrophic forgetting.

In this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model simultaneously identifies covariate associated components from covariance matrices, estimates regression coefficients, and estimates the within-subject variation in the covariance matrices. Optimal estimators are proposed for both low-dimensional and high-dimensional cases by maximizing the (approximated) hierarchical likelihood function and are proved to be asymptotically consistent, where the proposed estimator is the most efficient under the low-dimensional case and achieves the uniformly minimum quadratic loss among all linear combinations of the identity matrix and the sample covariance matrix under the high-dimensional case. Through extensive simulation studies, the proposed approach achieves good performance in identifying the covariate related components and estimating the model parameters. Applying to a longitudinal resting-state fMRI dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI), the proposed approach identifies brain networks that demonstrate the difference between males and females at different disease stages. The findings are in line with existing knowledge of AD and the method improves the statistical power over the analysis of cross-sectional data.

Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences., Comment: Accepted at the 2nd Conference on Lifelong Learning Agents (CoLLAs), 2023

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees handle more complex relationships among random variables and appear in many disciplines, such as brain imaging, genomics and finance. We consider the problem of sparse regression on data that are associated with a compositional tree and propose a transformation-free tree-based regularized regression method for component selection. The regularization penalty is designed based on the tree structure and encourages a sparse tree representation. We prove that our proposed estimator for regression coefficients is both consistent and model selection consistent. In the simulation study, our method shows higher accuracy than competing methods under different scenarios. By analyzing a brain imaging data set from studies of Alzheimer's disease, our method identifies meaningful associations between memory declination and volume of brain regions that are consistent with current understanding.

Brain segmentation at different levels is generally represented as hierarchical trees. Brain regional atrophy at specific levels was found to be marginally associated with Alzheimer's disease outcomes. In this study, we propose an L1-type regularization for predictors that follow a hierarchical tree structure. Considering a tree as a directed acyclic graph, we interpret the model parameters from a path analysis perspective. Under this concept, the proposed penalty regulates the total effect of each predictor on the outcome. With regularity conditions, it is shown that under the proposed regularization, the estimator of the model coefficient is consistent in L2-norm and the model selection is also consistent. By applying to a brain structural magnetic resonance imaging dataset acquired from the Alzheimer's Disease Neuroimaging Initiative, the proposed approach identifies brain regions where atrophy in these regions demonstrates the declination in memory. With regularization on the total effects, the findings suggest that the impact of atrophy on memory deficits is localized from small brain regions but at various levels of brain segmentation.

This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data are high dimensional, the normal likelihood function is ill-posed as the sample covariance matrix is rank-deficient. Thus, a well-conditioned linear shrinkage estimator of the covariance matrix is introduced. With multiple covariance matrices, the shrinkage coefficients are proposed to be common across matrices. Theoretical studies demonstrate that the proposed covariance matrix estimator is optimal achieving the uniformly minimum quadratic loss asymptotically among all linear combinations of the identity matrix and the sample covariance matrix. Under regularity conditions, the proposed estimator of the model parameters is consistent. The superior performance of the proposed approach over existing methods is illustrated through simulation studies. Implemented to a resting-state functional magnetic resonance imaging study acquired from the Alzheimer's Disease Neuroimaging Initiative, the proposed approach identified a brain network within which functional connectivity is significantly associated with Apolipoprotein E $\varepsilon$4, a strong genetic marker for Alzheimer's disease., Comment: 21 pages of main text and references, 3 figures

Independent component analysis is commonly applied to functional magnetic resonance imaging (fMRI) data to extract independent components (ICs) representing functional brain networks. While ICA produces reliable group-level estimates, single-subject ICA often produces noisy results. Template ICA (tICA) is a hierarchical ICA model using empirical population priors to produce reliable subject-level IC estimates. However, this and other hierarchical ICA models assume unrealistically that subject effects are spatially independent. Here, we propose spatial template ICA (stICA), which incorporates spatial process priors into tICA. This results in greater estimation efficiency of ICs and subject effects. Additionally, the joint posterior distribution can be used to identify engaged areas using an excursions set approach. By leveraging spatial dependencies and avoiding massive multiple comparisons, stICA has high power to detect true effects. We derive an efficient expectation-maximization algorithm to obtain maximum likelihood estimates of the model parameters and posterior moments of the latent fields. Based on analysis of simulated data and fMRI data from the Human Connectome Project, we find that stICA produces estimates that are more accurate and reliable than benchmark approaches, and identifies larger and more reliable areas of engagement. The algorithm is quite tractable, achieving convergence within 7 hours in our fMRI analysis., Comment: 32 pages, 16 figures

The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the characteristics of the data which are repeatable -- the aspects of the data that are able to be identified under a duplicated analysis. Conflictingly, the utility of traditional repeatability measures, such as the intraclass correlation coefficient, under these settings is limited. In recent work, novel data repeatability measures have been introduced in the context where a set of subjects are measured twice or more, including: fingerprinting, rank sums, and generalizations of the intraclass correlation coefficient. However, the relationships between, and the best practices among these measures remains largely unknown. In this manuscript, we formalize a novel repeatability measure, discriminability. We show that it is deterministically linked with the correlation coefficient under univariate random effect models, and has desired property of optimal accuracy for inferential tasks using multivariate measurements. Additionally, we overview and systematically compare repeatability statistics using both theoretical results and simulations. We show that the rank sum statistic is deterministically linked to a consistent estimator of discriminability. The power of permutation tests derived from these measures are compared numerically under Gaussian and non-Gaussian settings, with and without simulated batch effects. Motivated by both theoretical and empirical results, we provide methodological recommendations for each benchmark setting to serve as a resource for future analyses. We believe these recommendations will play an important role towards improving repeatability in fields such as functional magnetic resonance imaging, genomics, pharmacology, and more.

In severe viral pneumonia, including Coronavirus disease 2019 (COVID-19), the viral replication phase is often followed by hyperinflammation, which can lead to acute respiratory distress syndrome, multi-organ failure, and death. We previously demonstrated that alpha-1 adrenergic receptor ($\alpha_1$-AR) antagonists can prevent hyperinflammation and death in mice. Here, we conducted retrospective analyses in two cohorts of patients with acute respiratory distress (ARD, n=18,547) and three cohorts with pneumonia (n=400,907). Federated across two ARD cohorts, we find that patients exposed to $\alpha_1$-AR antagonists, as compared to unexposed patients, had a 34% relative risk reduction for mechanical ventilation and death (OR=0.70, p=0.021). We replicated these methods on three pneumonia cohorts, all with similar effects on both outcomes. All results were robust to sensitivity analyses. These results highlight the urgent need for prospective trials testing whether prophylactic use of $\alpha_1$-AR antagonists ameliorates lower respiratory tract infection-associated hyperinflammation and death, as observed in COVID-19., Comment: 31 pages, 10 figures

In this study, we propose a two-stage procedure for hypothesis testing, where the first stage is conventional hypothesis testing and the second is an equivalence testing procedure using an introduced Empirical Equivalence Bound. In 2016, the American Statistical Association released a policy statement on P-values to clarify the proper use and interpretation in response to the criticism of reproducibility and replicability in scientific findings. A recent solution to improve reproducibility and transparency in statistical hypothesis testing is to integrate P-values (or confidence intervals) with practical or scientific significance. Similar ideas have been proposed via the equivalence test, where the goal is to infer equality under a presumption (null) of inequality of parameters. However, in these testing procedures, the definition of scientific significance/equivalence can be subjective. To circumvent this drawback, we introduce a B-value and the Empirical Equivalence Bound, which are both estimated from the data. Performing a second-stage equivalence test, our procedure offers an opportunity to correct for false positive discoveries and improve the reproducibility in findings across studies.

With fast advancements in technologies, the collection of multiple types of measurements on a common set of subjects is becoming routine in science. Some notable examples include multimodal neuroimaging studies for the simultaneous investigation of brain structure and function, and multi-omics studies for combining genetic and genomic information. Integrative analysis of multimodal data allows scientists to interrogate new mechanistic questions. However, the data collection and generation of integrative hypotheses is outpacing available methodology for joint analysis of multimodal measurements. In this article, we study high-dimensional multimodal data integration in the context of mediation analysis. We aim to understand the roles different data modalities play as possible mediators in the pathway between an exposure variable and an outcome. We propose a mediation model framework with two data types serving as separate sets of mediators, and develop a penalized optimization approach for parameter estimation. We study both the theoretical properties of the estimator through an asymptotic analysis, and its finite-sample performance through simulations. We illustrate our method with a multimodal brain pathway analysis having both structural and functional connectivities as mediators in the association between sex and language processing.

Large brain imaging databases contain a wealth of information on brain organization in the populations they target, and on individual variability. While such databases have been used to study group-level features of populations directly, they are currently underutilized as a resource to inform single-subject analysis. Here, we propose leveraging the information contained in large functional magnetic resonance imaging (fMRI) databases by establishing population priors to employ in an empirical Bayesian framework. We focus on estimation of brain networks as source signals in independent component analysis (ICA). We formulate a hierarchical "template" ICA model where source signals---including known population brain networks and subject-specific signals---are represented as latent variables. For estimation, we derive an expectation maximization (EM) algorithm having an explicit solution. However, as this solution is computationally intractable, we also consider an approximate subspace algorithm and a faster two-stage approach. Through extensive simulation studies, we assess performance of both methods and compare with dual regression, a popular but ad-hoc method. The two proposed algorithms have similar performance, and both dramatically outperform dual regression. We also conduct a reliability study utilizing the Human Connectome Project and find that template ICA achieves substantially better performance than dual regression, achieving 75-250% higher intra-subject reliability.

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., Comment: 24 pages, 3 figures, 1 table

Causal mediation analysis is widely utilized to separate the causal effect of treatment into its direct effect on the outcome and its indirect effect through an intermediate variable (the mediator). In this study we introduce a functional mediation analysis framework in which the three key variables, the treatment, mediator, and outcome, are all continuous functions. With functional measures, causal assumptions and interpretations are not immediately well-defined. Motivated by a functional magnetic resonance imaging (fMRI) study, we propose two functional mediation models based on the influence of the mediator: (1) a concurrent mediation model and (2) a historical mediation model. We further discuss causal assumptions, and elucidate causal interpretations. Our proposed models enable the estimation of individual causal effect curves, where both the direct and indirect effects vary across time. Applied to a task-based fMRI study, we illustrate how our functional mediation framework provides a new perspective for studying dynamic brain connectivity. The R package cfma is available on CRAN.

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.

High-dimensional time-series data are becoming increasingly abundant across a wide variety of domains, spanning economics, neuroscience, particle physics, and cosmology. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these problems, due to both computational and statistical reasons. We mitigate both kinds of issues via proposing an M-estimator for Reduced-rank System IDentification (MR. SID). A combination of low-rank approximations, L-1 and L-2 penalties, and some numerical linear algebra tricks, yields an estimator that is computationally efficient and numerically stable. Simulations and real data examples demonstrate the utility of this approach in a variety of problems. In particular, we demonstrate that MR. SID can estimate spatial filters, connectivity graphs, and time-courses from native resolution functional magnetic resonance imaging data. Other applications and extensions are immediately available, as our approach is a generalization of the classical Kalman Filter-Smoother Expectation-Maximization algorithm.

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.

Much recent attention has been paid to quantifying anatomic and functional neuroimaging on the individual subject level. For optimal individual subject characterization, specific acquisition and analysis features need to be identified that maximize inter-individual variability while concomitantly minimizing intra-subject variability. Here we develop a non-parametric statistical metric that quantifies the degree to which a parameter set allows this individual subject differentiation. We apply this metric to analyzing publicly available test-retest resting-state fMRI (rs-fMRI) data sets. We find that for the question of maximizing individual differentiation, there is a relative tradeoff between increasing sampling through increased sampling frequency or increased acquisition time; that for the sizes of the interrogated data sets, only 4-5 min of acquisition time is necessary to perfectly differentiate each subject; and that brain regions that most contribute to individuals unique characterization lie in association cortices thought to contribute to higher cognitive function. These findings may guide optimal rs-fMRI experiment design and may aid elucidation of the neural bases for subject-to-subject differences., Comment: 14 pages, 5 figures

We develop a flexible framework for modeling high-dimensional imaging data observed longitudinally. The approach decomposes the observed variability of repeatedly measured high-dimensional observations into three additive components: a subject-specific imaging random intercept that quantifies the cross-sectional variability, a subject-specific imaging slope that quantifies the dynamic irreversible deformation over multiple realizations, and a subject-visit-specific imaging deviation that quantifies exchangeable effects between visits. The proposed method is very fast, scalable to studies including ultrahigh-dimensional data, and can easily be adapted to and executed on modest computing infrastructures. The method is applied to the longitudinal analysis of diffusion tensor imaging (DTI) data of the corpus callosum of multiple sclerosis (MS) subjects. The study includes $176$ subjects observed at $466$ visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 30,000 voxels., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS748 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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%., Comment: body 21 pages, 11 figures

This manuscript uses machine learning techniques to exploit baseball pitchers' decision making, so-called "Baseball IQ," by modeling the at-bat information, pitch selection and counts, as a Markov Decision Process (MDP). Each state of the MDP models the pitcher's current pitch selection in a Markovian fashion, conditional on the information immediately prior to making the current pitch. This includes the count prior to the previous pitch, his ensuing pitch selection, the batter's ensuing action and the result of the pitch., Comment: Published in at http://dx.doi.org/10.1214/13-AOAS712 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ($p$) is much larger than the number of subjects ($n$), the challenge of calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same $n$-dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same $n$-dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the $p$-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram (EEG) recordings ($p=900$, $n=392$), and to a dataset of brain magnetic resonance images (MRIs) ($p\approx$ 3 million, $n=352$). For the brain MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods., Comment: 25 pages, including 9 figures and link to R package. 2014-05-14 update: final formatting edits for journal submission, condensed figures

Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two steps. First is a feature extraction by summarizing measurements within a parcellation, regional or set definition to create nodes. Secondly, these summaries are then used to create a graph representing relationships of interest. In this manuscript we study the impact of dimension reduction on graphs that describe different notions of relations among a set of random variables. We are particularly interested in undirected graphs that capture the random variables' independence and conditional independence relations. A dimension reduction procedure can be any mapping from high dimensional spaces to low dimensional spaces. We exploit a general framework for modeling the raw data and advocate that in estimating the undirected graphs, any acceptable dimension reduction procedure should be a graph-homotopic mapping, i.e., the graphical structure of the data after dimension reduction should inherit the main characteristics of the graphical structure of the raw data. We show that, in terms of inferring undirected graphs that characterize the conditional independence relations among random variables, many dimension reduction procedures, such as the mean, median, or principal components, cannot be theoretically guaranteed to be a graph-homotopic mapping. The implications of this work are broad. In the most charitable setting for researchers, where the correct node definition is known, graphical relationships can be contaminated merely via the dimension reduction. The manuscript ends with a concrete example, characterizing a subset of graphical structures such that the dimension reduction procedure using the principal components can be a graph-homotopic mapping., Comment: 19 pages

Data reproducibility is a critical issue in all scientific experiments. In this manuscript, we consider the problem of quantifying the reproducibility of graphical measurements. We generalize the concept of image intra-class correlation coefficient (I2C2) and propose the concept of the graphical intra-class correlation coefficient (GICC) for such purpose. The concept of GICC is based on multivariate probit-linear mixed effect models. We will present a Markov Chain EM (MCEM) algorithm for estimating the GICC. Simulations results with varied settings are demonstrated and our method is applied to the KIRBY21 test-retest dataset., Comment: 14 pages, 3 figures, 1 table

In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T,n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method., Comment: 40 pages

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Utilizing the concept of median graphs in summarizing the commonality across these graphical structures, a novel semiparametric approach to modeling such complex aggregated data is provided along with robust estimation of the median graph, which is assumed to be sparse. The estimator is proved to be consistent in graph recovery and an upper bound on the rate of convergence is given. Experiments on both synthetic and real datasets are conducted to illustrate the empirical usefulness of the proposed models and methods.

In this manuscript, we are concerned with data generated from a diffusion tensor imaging (DTI) experiment. The goal is to parameterize manifold-like white matter tracts, such as the corpus callosum, using principal surfaces. We approach the problem by finding a geometrically motivated surface-based representation of the corpus callosum and visualize the fractional anisotropy (FA) values projected onto the surface; the method applies to any other diffusion summary as well as to other white matter tracts. We provide an algorithm that 1) constructs the principal surface of a corpus callosum; 2) flattens the surface into a parametric 2D map; 3) projects associated FA values on the map. The algorithm was applied to a longitudinal study containing 466 diffusion tensor images of 176 multiple sclerosis (MS) patients observed at multiple visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 20,000 voxels. Extensive simulation studies demonstrate fast convergence and robust performance of the algorithm under a variety of challenging scenarios., Comment: 27 pages, 5 figures and 1 table

Independent Component Analysis (ICA) is a computational technique for revealing latent factors that underlie sets of measurements or signals. It has become a standard technique in functional neuroimaging. In functional neuroimaging, so called group ICA (gICA) seeks to identify and quantify networks of correlated regions across subjects. This paper reports on the development of a new group ICA approach, Homotopic Group ICA (H-gICA), for blind source separation of resting state functional magnetic resonance imaging (fMRI) data. Resting state brain functional homotopy is the similarity of spontaneous fluctuations between bilaterally symmetrically opposing regions (i.e. those symmetric with respect to the mid-sagittal plane) (Zuo et al., 2010). The approach we proposed improves network estimates by leveraging this known brain functional homotopy. H-gICA increases the potential for network discovery, effectively by averaging information across hemispheres. It is theoretically proven to be identical to standard group ICA when the true sources are both perfectly homotopic and noise-free, while simulation studies and data explorations demonstrate its benefits in the presence of noise. Moreover, compared to commonly applied group ICA algorithms, the structure of the H-gICA input data leads to significant improvement in computational efficiency. A simulation study comfirms its effectiveness in homotopic, non-homotopic and mixed settings, as well as on the landmark ADHD-200 dataset. From a relatively small subset of data, several brain networks were found including: the visual, the default mode and auditory networks, as well as others. These were shown to be more contiguous and clearly delineated than the corresponding ordinary group ICA. Finally, in addition to improving network estimation, H-gICA facilitates the investigation of functional homotopy via ICA-based networks., Comment: 35 pages, 13 figures

We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT) and to a white-matter tract image produced using diffusion tensor imaging (DTI)., Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilevel functional principal component analysis (MFPCA), a novel statistical methodology designed to extract core intra- and inter-subject geometric components of multilevel functional data. Though motivated by the SHHS, the proposed methodology is generally applicable, with potential relevance to many modern scientific studies of hierarchical or longitudinal functional outcomes. Notably, using MFPCA, we identify and quantify associations between EEG activity during sleep and adverse cardiovascular outcomes., Comment: Published in at http://dx.doi.org/10.1214/08-AOAS206 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in a variety of examples.