Wavelet transform for large dimension Gaussian Process regression

Gaussian process models can capture complex structures in many
statistical learning examples. However, constructing surrogate models
for uncertainty quantification on high-dimensional output with Gaussian
processes is highly challenging. Nevertheless, there are efficient
tools to overcome the curse of dimensionality for specific applications
and in particular the wavelet transform. This work proposes a new
framework using wavelets for Gaussian process regression. Gaussian
processes in a wavelet domain, unlike other methods, provide an
analytical framework that is computationally robust. The novelty of
this work is to propose an analytical expression for the covariance
function in wavelet space, for both the continuous and discrete cases.
A second development is the selection of conditioning points in latent
space during wavelet Gaussian process regression. The proposed method
is compared with neural network methods and singular decomposition
methods, an analytical function and a simple code example.