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Full-Text Articles in Physical Sciences and Mathematics
Massively Parallel Nonparametric Regression, With An Application To Developmental Brain Mapping, Philip T. Reiss, Lei Huang, Yin-Hsiu Chen, Lan Huo, Thaddeus Tarpey, Maarten Mennes
Massively Parallel Nonparametric Regression, With An Application To Developmental Brain Mapping, Philip T. Reiss, Lei Huang, Yin-Hsiu Chen, Lan Huo, Thaddeus Tarpey, Maarten Mennes
Lei Huang
We propose a penalized spline approach to performing large numbers of parallel nonparametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naively performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at …
Smoothness Selection For Penalized Quantile Regression Splines, Philip T. Reiss, Lei Huang
Smoothness Selection For Penalized Quantile Regression Splines, Philip T. Reiss, Lei Huang
Philip T. Reiss
Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as …
Resampling-Based Information Criteria For Best-Subset Regression, Philip T. Reiss, Lei Huang, Joseph E. Cavanaugh, Amy Krain Roy
Resampling-Based Information Criteria For Best-Subset Regression, Philip T. Reiss, Lei Huang, Joseph E. Cavanaugh, Amy Krain Roy
Philip T. Reiss
When a linear model is chosen by searching for the best subset among a set of candidate predictors, a fixed penalty such as that imposed by the Akaike information criterion may penalize model complexity inadequately, leading to biased model selection. We study resampling-based information criteria that aim to overcome this problem through improved estimation of the effective model dimension. The first proposed approach builds upon previous work on bootstrap-based model selection. We then propose a more novel approach based on cross-validation. Simulations and analyses of a functional neuroimaging data set illustrate the strong performance of our resampling-based methods, which are …
Extracting Information From Functional Connectivity Maps Via Function-On-Scalar Regression, Philip T. Reiss, Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, Michael P. Milham
Extracting Information From Functional Connectivity Maps Via Function-On-Scalar Regression, Philip T. Reiss, Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, Michael P. Milham
Lei Huang
Functional connectivity of an individual human brain is often studied by acquiring a resting state functional magnetic resonance imaging scan, and mapping the correlation of each voxel's BOLD time series with that of a seed region. As large collections of such maps become available, including multisite data sets, there is an increasing need for ways to distill the information in these maps in a readily visualized form. Here we propose a two-step analytic strategy. First, we construct connectivity-distance profiles, which summarize the connectivity of each voxel in the brain as a function of distance from the seed, a functional relationship …
Extracting Information From Functional Connectivity Maps Via Function-On-Scalar Regression, Philip T. Reiss, Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, Michael P. Milham
Extracting Information From Functional Connectivity Maps Via Function-On-Scalar Regression, Philip T. Reiss, Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, Michael P. Milham
Philip T. Reiss
Functional connectivity of an individual human brain is often studied by acquiring a resting state functional magnetic resonance imaging scan, and mapping the correlation of each voxel's BOLD time series with that of a seed region. As large collections of such maps become available, including multisite data sets, there is an increasing need for ways to distill the information in these maps in a readily visualized form. Here we propose a two-step analytic strategy. First, we construct connectivity-distance profiles, which summarize the connectivity of each voxel in the brain as a function of distance from the seed, a functional relationship …
Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes
Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes
Lei Huang
Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …
Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes
Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes
Philip T. Reiss
Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …