Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional ( @math ) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the @math -norm of the signal in high-dimensional linear regression. We derive a novel procedure for this, which is asymptotically correct when the covariates are multivariate Gaussian and produces valid confidence intervals in finite samples as well. The procedure, called EigenPrism, is computationally fast and makes no assumptions on coefficient sparsity or knowledge of the noise level. We investigate the width of the EigenPrism confidence intervals, including a comparison with a Bayesian setting in which our interval is just 5 wider than the Bayes credible interval. We are then able to unify the three aforementioned problems by showing that the EigenPrism procedure with only minor modifications is able to make important contributions to all three. We also investigate the robustness of coverage and find that the method applies in practice and in finite samples much more widely than just the case of multivariate Gaussian covariates. Finally, we apply EigenPrism to a genetic dataset to estimate the genetic signal-to-noise ratio for a number of continuous phenotypes.
We note that neuroscientists have also done work estimating a signal-to-noise ratio, namely the explainable variance in functional MRI. That problem is made especially challenging due to correlations in the noise, making it different from the i.i.d. noise setting considered in this paper. For this related problem, @cite_9 are able to construct an unbiased estimator in the random effects framework by permuting the measurement vector in such a way as to leave the noise covariance structure unchanged.
@cite_9
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Neuroimagery must be visually checked for unacceptable levels of distortion prior to processing. However, inspection is time-consuming, unreliable for detecting subtle distortions and often subjective. With the increasing volume of neuroimagery, objective measures of quality are needed in order to automate screening. To address this need, we have assessed the effectiveness of no-reference image quality measures, which quantify quality inherent to a single image. A data set of 1001 magnetic resonance images (MRIs) recorded from 143 subjects was used for this evaluation. The MRI images were artificially distorted with two levels of either additive Gaussian noise or intensity nouniformity created from a linear model. A total of 239 different quality measures were defined from seven overall families and used to discriminate images for the type and level of distortion. Analysis of Variance identified two families of quality measure that were most effective: one based on Natural Scene Statistics and one originally developed to measure distortion caused by image compression. Measures from both families reliably discriminated among undistorted images, noisy images, and images distorted by intensity nonuniformity. The best quality measures were sensitive only to the distortion category and were not significantly affected by other factors. The results are encouraging enough that several quality measures are being incorporated in a real world MRI test bed. Abstract Brain extraction from magnetic resonance imaging (MRI) is crucial for many neuroimaging workflows. Current methods demonstrate good results on non-enhanced T1-weighted images, but struggle when confronted with other modalities and pathologically altered tissue. In this paper we present a 3D convolutional deep learning architecture to address these shortcomings. In contrast to existing methods, we are not limited to non-enhanced T1w images. When trained appropriately, our approach handles an arbitrary number of modalities including contrast-enhanced scans. Its applicability to MRI data, comprising four channels: non-enhanced and contrast-enhanced T1w, T2w and FLAIR contrasts, is demonstrated on a challenging clinical data set containing brain tumors (N = 53), where our approach significantly outperforms six commonly used tools with a mean Dice score of 95.19. Further, the proposed method at least matches state-of-the-art performance as demonstrated on three publicly available data sets: IBSR, LPBA40 and OASIS, totaling N = 135 volumes. For the IBSR (96.32) and LPBA40 (96.96) data set the convolutional neuronal network (CNN) obtains the highest average Dice scores, albeit not being significantly different from the second best performing method. For the OASIS data the second best Dice (95.02) results are achieved, with no statistical difference in comparison to the best performing tool. For all data sets the highest average specificity measures are evaluated, whereas the sensitivity displays about average results. Adjusting the cut-off threshold for generating the binary masks from the CNN's probability output can be used to increase the sensitivity of the method. Of course, this comes at the cost of a decreased specificity and has to be decided application specific. Using an optimized GPU implementation predictions can be achieved in less than one minute. The proposed method may prove useful for large-scale studies and clinical trials. In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence of nuisance parameters and noise. Motivated by such challenges, we consider the problem of estimating a signal from its scaled, cyclically-shifted and noisy observations. We focus on the particularly challenging regime of low signal-to-noise ratio (SNR), where different observations cannot be shift-aligned. We show that an accurate estimation of the signal from its noisy observations is possible, and derive a procedure which is proved to consistently estimate the signal. The asymptotic sample complexity (the number of observations required to recover the signal) of the procedure is @math . Additionally, we propose a procedure which is experimentally shown to improve the sample complexity by a factor equal to the signal's length. Finally, we present numerical experiments which demonstrate the performance of our algorithms, and corroborate our theoretical findings. This paper introduces two unsupervised learning methods for analyzing functional magnetic resonance imaging (fMRI) data based on hidden Markov model (HMM). HMM approach is focused on capturing the first-order statistical evolution among the samples of a voxel time series, and it can provide a complimentary perspective of the BOLD signals. Two-state HMM is created for each voxel, and the model parameters are estimated from the voxel time series and the stimulus paradigm. Two different activation detection methods are presented in this paper. The first method is based on the likelihood and likelihood-ratio test, in which an additional Gaussian model is used to enhance the contrast of the HMM likelihood map. The secondmethod is based on certain distance measures between the two state distributions, in which the most likely HMM state sequence is estimated through the Viterbi algorithm. The distance between the on-state and off-state distributions is measured either through a t-test, or using the Kullback-Leibler distance (KLD). Experimental results on both normal subject and brain tumor subject are presented. HMM approach appears to be more robust in detecting the supplemental active voxels comparing with SPM, especially for brain tumor subject.