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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 …
Varying-Smoother Models For Functional Responses, Philip T. Reiss, Lei Huang, Huaihou Chen, Stan Colcombe
Varying-Smoother Models For Functional Responses, Philip T. Reiss, Lei Huang, Huaihou Chen, Stan Colcombe
Philip T. Reiss
This paper studies estimation of a smooth function f(x,v) when we are given functional responses of the form f(x, ·) + error, but scientific interest centers on the collection of functions f(·,v) for different v. The motivation comes from studies of human brain development, in which x denotes age whereas v refers to brain locations. Analogously to varying-coefficient models, in which the mean response is linear in x, the “varying-smoother” models that we consider exhibit nonlinear dependence on x that varies smoothly with v. We discuss three approaches to estimating varying-smoother models: (a) methods that employ a tensor product penalty; …