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Penalized nonparametric scalar-on-function regression via principal coordinates.

Philip T Reiss1, David L Miller2, Pei-Shien Wu3

  • 1Department of Child and Adolescent Psychiatry and Department of Population Health, New York University, USA and Department of Statistics, University of Haifa, Israel.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|December 9, 2017
PubMed
Summary
This summary is machine-generated.

Principal coordinate ridge regression is a new nonparametric method for scalar-on-function regression. This approach outperforms existing methods in signature verification tasks.

Keywords:
dynamic time warpingfunctional regressiongeneralized additive modelkernel ridge regressionmultidimensional scaling

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Classical nonparametric regression methods are being extended to handle functional predictors.
  • Scalar-on-function regression is a key area in statistical modeling.

Purpose of the Study:

  • Introduce a novel nonparametric regression method for scalar-on-function analysis.
  • Extend intermediate-rank penalized smoothing to functional data.
  • Develop a method that is computationally efficient and extensible.

Main Methods:

  • Propose Principal Coordinate Ridge Regression (PCRR).
  • Regress response on leading principal coordinates derived from functional predictor distances.
  • Apply a ridge penalty for regularization.
  • Utilize generalized additive modeling for implementation and tuning.

Main Results:

  • PCRR demonstrates superior performance compared to functional generalized linear models in signature verification.
  • The method allows for fast optimal tuning parameter selection.
  • The implementation supports extensions to multiple functional predictors, various response types, and mixed-effects models.

Conclusions:

  • Principal Coordinate Ridge Regression is an effective extension of penalized smoothing for scalar-on-function regression.
  • The proposed method offers advantages in performance and flexibility.
  • The publicly available implementation facilitates practical application and further research.