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

arXiv: https://arxiv.org/abs/1604.03192 · HTML: https://mlsanity.com/paper/1604.03192/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2016.

## Built on by (most cited first, 12 of 12)

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- [Deep Kronecker Network](https://mlsanity.com/paper/2210.13327/) (2022)
- [T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs](https://mlsanity.com/paper/2107.02510/) (2021)
- [Robust High-Dimensional Regression with Coefficient Thresholding and its Application to Imaging Data Analysis](https://mlsanity.com/paper/2109.14856/) (2021)
- [Statistical Opportunities in Neuroimaging](https://mlsanity.com/paper/2602.12974/) (2026)
- [Bayesian temporal biclustering with applications to multi-subject neuroscience studies](https://mlsanity.com/paper/2406.17131/) (2024)
- [Time Series Generative Learning with Application to Brain Imaging Analysis](https://mlsanity.com/paper/2407.14003/) (2024)
- [Sparse Bayesian Modeling of EEG Channel Interactions Improves P300 Brain-Computer Interface Performance](https://mlsanity.com/paper/2602.17772/) (2026)
- [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026)
- [Additive Nonparametric Regression with Spatial and Network Objects](https://mlsanity.com/paper/2609.26867/) (2026)

## Abstract (arXiv)

The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms. Theoretically, soft-thresholded Gaussian processes provide large prior support for the spatially varying coefficients that enjoy piecewise smoothness, sparsity and continuity, characterizing the important features of imaging data. Also, under some mild regularity conditions, the soft-thresholded Gaussian process leads to the posterior consistency for both parameter estimation and variable selection for scalar-on-image regression, even when the number of true predictors is larger than the sample size. The proposed method is illustrated via simulations, compared numerically with existing alternatives and applied to Electroencephalography (EEG) study of alcoholism.