Search

In this study, we consider the problem of regressing covariance matrices on associated covariates. Our goal is to use covariates to explain variation in covariance matrices across units. As such, we introduce Covariate Assisted Principal (CAP) regression, an optimization-based method for identifying components associated with the covariates using a generalized linear model approach. We develop computationally efficient algorithms to jointly search for common linear projections of the covariance matrices, as well as the regression coefficients. Under the assumption that all the covariance matrices share identical eigencomponents, we establish the asymptotic properties. In simulation studies, our CAP method shows higher accuracy and robustness in coefficient estimation over competing methods. In an example resting-state functional magnetic resonance imaging study of healthy adults, CAP identifies human brain network changes associated with subject demographics., (© The Author 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

We examine differences between independent component analyses (ICAs) arising from different assumptions, measures of dependence, and starting points of the algorithms. ICA is a popular method with diverse applications including artifact removal in electrophysiology data, feature extraction in microarray data, and identifying brain networks in functional magnetic resonance imaging (fMRI). ICA can be viewed as a generalization of principal component analysis (PCA) that takes into account higher-order cross-correlations. Whereas the PCA solution is unique, there are many ICA methods-whose solutions may differ. Infomax, FastICA, and JADE are commonly applied to fMRI studies, with FastICA being arguably the most popular. Hastie and Tibshirani (2003) demonstrated that ProDenICA outperformed FastICA in simulations with two components. We introduce the application of ProDenICA to simulations with more components and to fMRI data. ProDenICA was more accurate in simulations, and we identified differences between biologically meaningful ICs from ProDenICA versus other methods in the fMRI analysis. ICA methods require nonconvex optimization, yet current practices do not recognize the importance of, nor adequately address sensitivity to, initial values. We found that local optima led to dramatically different estimates in both simulations and group ICA of fMRI, and we provide evidence that the global optimum from ProDenICA is the best estimate. We applied a modification of the Hungarian (Kuhn-Munkres) algorithm to match ICs from multiple estimates, thereby gaining novel insights into how brain networks vary in their sensitivity to initial values and ICA method., (© 2013, The International Biometric Society.)

Independent component analysis (ICA) is a widely used technique for blind source separation, used heavily in several scientific research areas including acoustics, electrophysiology, and functional neuroimaging. We propose a scalable two-stage iterative true group ICA methodology for analyzing population level functional magnetic resonance imaging (fMRI) data where the number of subjects is very large. The method is based on likelihood estimators of the underlying source densities and the mixing matrix. As opposed to many commonly used group ICA algorithms, the proposed method does not require significant data reduction by a 2-fold singular value decomposition. In addition, the method can be applied to a large group of subjects since the memory requirements are not restrictive. The performance of our approach is compared with a commonly used group ICA algorithm via simulation studies. Furthermore, the proposed method is applied to a large collection of resting state fMRI datasets. The results show that established brain networks are well recovered by the proposed algorithm.

Functional connectivity is the study of correlations in measured neurophysiological signals. Altered functional connectivity has been shown to be associated with a variety of cognitive and memory impairments and dysfunction, including Alzheimer's disease. In this manuscript we use a two-stage application of the singular value decomposition to obtain data driven population-level measures of functional connectivity in functional magnetic resonance imaging (fMRI). The method is computationally simple and amenable to high dimensional fMRI data with large numbers of subjects. Simulation studies suggest the ability of the decomposition methods to recover population brain networks and their associated loadings. We further demonstrate the utility of these decompositions in a functional logistic regression model. The method is applied to a novel fMRI study of Alzheimer's disease risk under a verbal paired associates task. We found an indication of alternative connectivity in clinically asymptomatic at-risk subjects when compared to controls, which was not significant in the light of multiple comparisons adjustment. The relevant brain network loads primarily on the temporal lobe and overlaps significantly with the olfactory areas and temporal poles., (Copyright (c) 2010 Elsevier Inc. All rights reserved.)

The ideal observer (IO) employs complete knowledge of the available data statistics and sets an upper limit on observer performance on a binary classification task. However, the IO test statistic cannot be calculated analytically, except for cases where object statistics are extremely simple. Kupinski have developed a Markov chain Monte Carlo (MCMC) based technique to compute the IO test statistic for, in principle, arbitrarily complex objects and imaging systems. In this work, we applied MCMC to estimate the IO test statistic in the context of myocardial perfusion SPECT (MPS). We modeled the imaging system using an analytic SPECT projector with attenuation, distant-dependent detector-response modeling and Poisson noise statistics. The object is a family of parameterized torso phantoms with variable geometric and organ uptake parameters. To accelerate the imaging simulation process and thus enable the MCMC IO estimation, we used discretized anatomic parameters and continuous uptake parameters in defining the objects. The imaging process simulation was modeled by precomputing projections for each organ for a finite number of discretely-parameterized anatomic parameters and taking linear combinations of the organ projections based on continuous sampling of the organ uptake parameters. The proposed method greatly reduces the computational burden and allows MCMC IO estimation for a realistic MPS imaging simulation. We validated the proposed IO estimation technique by estimating IO test statistics for a large number of input objects. The properties of the first- and second-order statistics of the IO test statistics estimated using the MCMC IO estimation technique agreed well with theoretical predictions. Further, as expected, the IO had better performance, as measured by the receiver operating characteristic (ROC) curve, than the Hotelling observer. This method is developed for SPECT imaging. However, it can be adapted to any linear imaging system.

Nuisance parameters are parameters that are not of immediate interest to the experimenter. For log-linear and logistic models the null distribution of (most) statistics of interest depends on such parameters. Traditionally, nuisance parameters were eliminated by performing inference with respect to the chi-squared limiting distribution of common test statistics. An alternative solution is to eliminate the nuisance parameters by conditioning on their minimal sufficient statistics. The support of the resulting conditional distribution is often intractable, making null probability calculations challenging. An often feasible way to avoid complete enumeration of this support is to approximate conditional probabilities using Monte Carlo methods. In this article we survey recent developments in Monte Carlo conditional analysis for log-linear and logistic models focusing on the algorithms proposed by Booth and Butler, Diaconis and Sturmfels, Smith et al., and Mehta et al. We illustrate these algorithms with simple motivating examples.