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

Research output: Contribution to journalArticlepeer-review


A penalized approach is proposed for 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 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 70,000 brain locations. Supplementary materials, including an appendix and an R package, are available online.

Original languageEnglish
Pages (from-to)232-248
Number of pages17
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - 2014
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank Eva Petkova, Ciprian Crainiceanu, Davide Imperati, Michael Milham, Clare Kelly, Babak Ardekani, and Xavier Castellanos for very helpful discussions; and the Editor, Associate Editor, and referees for valuable comments on the initial manuscript. The first author’s research is supported in part by National Science Foundation grant DMS-0907017 and National Institutes of Health grant 1R01MH095836-01A1.


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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