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Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process.

Jian Kang1, Brian J Reich2, Ana-Maria Staicu3

  • 1Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A. jiankang@umich.edu.

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This study introduces a new Bayesian model for spatial variable selection in scalar-on-image regression. The method effectively identifies relevant predictors, even with more variables than data points.

Keywords:
ElectroencephalographyGaussian processesPosterior consistencySpatial variable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Neuroscience

Background:

  • Scalar-on-image regression is crucial for analyzing neuroimaging data.
  • Selecting relevant spatial variables is challenging due to high dimensionality.

Purpose of the Study:

  • To develop a novel Bayesian nonparametric model for spatial variable selection in scalar-on-image regression.
  • To ensure accurate parameter estimation and variable selection, even in high-dimensional settings.

Main Methods:

  • Proposed a new class of Bayesian nonparametric models.
  • Developed an efficient posterior computational algorithm.
  • Utilized a soft-thresholded Gaussian process prior for piecewise-smooth, sparse, and continuous spatially-varying coefficients.

Main Results:

  • The soft-thresholded Gaussian process prior supports sparse and continuous spatial coefficients.
  • Demonstrated posterior consistency for parameter estimation and variable selection.
  • Outperformed alternative methods in simulations and an electroencephalography study.

Conclusions:

  • The proposed Bayesian method offers robust spatial variable selection for scalar-on-image regression.
  • Effective even when the number of predictors exceeds the sample size.
  • Applicable to real-world neuroimaging data analysis, such as in alcoholism studies.