Spatial shrinkage via the product independent Gaussian process prior

05/08/2018
by   Arkaprava Roy, et al.
0

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise smooth as product of independent Gaussian processes (PING) with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process shows more components in the product results in thicker tail and sharper peak at zero. The simulation results demonstrate the improvement in estimation using the PING prior over Gaussian process (GP) prior for different image regressions. We apply our method to a longitudinal MRI dataset to detect the regions that are affected by multiple sclerosis (MS) in the greatest magnitude through an image-on-scalar regression model. Due to huge dimensionality of these images, we transform the data into the spectral domain and develop methods to conduct computation in this domain. In our MS imaging study, the estimates from the PING model are more informative than those from the GP model.

READ FULL TEXT

page 32

page 36

page 39

research
04/18/2012

EigenGP: Sparse Gaussian process models with data-dependent eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of funct...
research
03/13/2018

Variational zero-inflated Gaussian processes with sparse kernels

Zero-inflated datasets, which have an excess of zero outputs, are common...
research
11/27/2020

Knowledge transfer across cell lines using Hybrid Gaussian Process models with entity embedding vectors

To date, a large number of experiments are performed to develop a bioche...
research
11/08/2020

Skewed Laplace Spectral Mixture kernels for long-term forecasting in Gaussian process

Long-term forecasting involves predicting a horizon that is far ahead of...
research
11/21/2016

Variational Fourier features for Gaussian processes

This work brings together two powerful concepts in Gaussian processes: t...
research
02/21/2018

Subspace-Induced Gaussian Processes

We present a new Gaussian process (GP) regression model where the covari...
research
03/28/2021

Gaussian Process Convolutional Dictionary Learning

Convolutional dictionary learning (CDL), the problem of estimating shift...

Please sign up or login with your details

Forgot password? Click here to reset