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J Comput Graph Stat. 2014 Jan 1;23(1):232-248.

Massively parallel nonparametric regression, with an application to developmental brain mapping.

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Department of Child and Adolescent Psychiatry, New York University ; Nathan S. Kline Institute for Psychiatric Research.
Department of Biostatistics, Johns Hopkins University.
Department of Child and Adolescent Psychiatry, New York University.
Department of Mathematics and Statistics, Wright State University.
Department of Cognitive Neuroscience, Radboud University Nijmegen Medical Centre ; Department of Child and Adolescent Psychiatry, New York University.


We propose a penalized spline approach to performing large numbers of parallel non-parametric 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 naïvely 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 each of approximately 70000 brain locations. Supplementary materials, including an appendix and an R package, are available online.


Functional data clustering; Neuroimaging; Penalized splines; Restricted likelihood ratio test; Smoothing parameter selection

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