1,720,971 research outputs found
Generalized Procrustes problem allows to estimate subject-specific functional connectivity in fMRI data
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How active is a genetic pathway? Comparative analysis of post-hoc permutation-based methods
No full textProcedures with true discovery guarantee, i.e., methods for simultaneous inference on
the True Discovery Proportion (TDP), have become widely popular in many applications. They permit addressing the multiplicity problem while at the same time solving the spatial specificity paradox. Here we propose a comparative analysis of some of the most widely used permutation-based procedures: sumSome, pARI, sansSouci and Notip. We compare their performance on differential gene expression data analysis, where the interest lies in quantifying levels of activation in different pathways
Permutation-based true discovery proportions for functional magnetic resonance imaging cluster analysis
Full text linkWe propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously valid with high confidence. The methodology is particularly useful in functional Magnetic Resonance Imaging cluster analysis, where it provides a confidence statement on the percentage of truly activated voxels within clusters of voxels, avoiding the well-known spatial specificity paradox. We offer a user-friendly tool to estimate the percentage of true discoveries for each cluster while controlling the family-wise error rate for multiple testing and taking into account that the cluster was chosen in a data-driven way. The method adapts to the spatial correlation structure that characterizes functional Magnetic Resonance Imaging data, gaining power over parametric approaches
Procrustes analysis for high-dimensional data
Full text linkThe Procrustes-based perturbation model (Goodall, 1991) allows minimization
of the Frobenius distance between matrices by similarity transformation.
However, it suffers from non-identifiability, critical interpretation of the
transformed matrices, and inapplicability in high-dimensional data. We provide
an extension of the perturbation model focused on the high-dimensional data
framework, called the ProMises (Procrustes von Mises-Fisher) model. The
ill-posed and interpretability problems are solved by imposing a proper prior
distribution for the orthogonal matrix parameter (i.e., the von Mises-Fisher
distribution) which is a conjugate prior, resulting in a fast estimation
process. Furthermore, we present the Efficient ProMises model for the
high-dimensional framework, useful in neuroimaging, where the problem has much
more than three dimensions. We found a great improvement in functional magnetic
resonance imaging (fMRI) connectivity analysis because the ProMises model
permits incorporation of topological brain information in the alignment's
estimation process.Comment: 22 pages, 7 figure
Functional alignment by the "light" approach of the von Mises-Fisher-Procrustes model.
No full textProcrustes-based methods involve the singular value decomposition of a square matrix, leading to polynomial time complexity, and requiring a considerable memory for large-scale problems. Procrustes-based methods are used as functional alignment for fMRI data in the multi-subjects analysis. A high-dimensional matrix expresses the subject’s neural activation, and Procrustes-based methods are infeasible (computationally). The alignment can be conducted only on regions of interest of the brain. We proposed a “light” version of the Procrustes-based methods. A semi-orthogonal transformation reduces the matrices’ dimension before applying the Procrustes alignment, maintaining the variability of the matrix that enters in the decomposition step. fMRI application shows a low decrease in predictive performance
Valid double-dipping via permutation-based closed testing
No full textFunctional Magnetic Resonance Imaging (fMRI) cluster analysis is widely popular for finding neural activation associated with some stimulus. However, it suffers from the spatial specificity paradox, and making follow-up inference inside clusters is not allowed. Valid double-dipping can be performed by closed testing, which determines lower confidence bounds for the number of active voxels, simultaneously over all regions. Moreover, a permutation framework adapts to the unknown joint distribution of the data. In the fMRI context, we evaluate two methods that rely on closed testing and permutations: permutation-based true discovery guarantee by sum tests, and permutation-based All-Resolutions Inference
Resampling-based inference for high-dimensional regression
No full textWe propose a novel procedure for resampling-based multiple testing in high-dimensional regression. First, we construct permutation test statistics for each individual hypothesis by means of repeated random splits of the data. In each split, half of the observations is used to perform variable selection, and half to build test statistics for the selected variables. Then we define an asymptotically exact test for any subset of hypotheses by aggregating the individual statistics through a suitable function, e.g., maximum or weighted sums. The procedure is flexible, allowing different selection techniques and combining functions. It can be embedded into closed testing methods to make simultaneous confidence statements on the proportion of true discoveries (TDP) of all subsets, valid even under post-hoc selection
Procrustes-based distances for exploring between-matrices similarity
Full text linkThe statistical shape analysis called Procrustes analysis minimizes the Frobenius distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This manuscript presents two types of distances derived from Procrustes analysis for exploring between-matrices similarity. The first one focuses on the residuals from the Procrustes analysis, i.e., the residual-based distance metric. In contrast, the second one exploits the fitted orthogonal matrices, i.e., the rotational-based distance metric. Thanks to these distances, similarity-based techniques such as the multidimensional scaling method can be applied to visualize and explore patterns and similarities among observations. The proposed distances result in being helpful in functional magnetic resonance imaging (fMRI) data analysis. The brain activation measured over space and time can be represented by a matrix. The proposed distances applied to a sample of subjects—i.e., matrices—revealed groups of individuals sharing patterns of neural brain activation. Finally, the proposed method is useful in several contexts when the aim is to analyze the similarity between high-dimensional matrices affected by functional misalignment
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