We present a new strategy for learning the functional relation between a pair
of variables, while addressing inhomogeneities in the correlation structure of
the available data, by modelling the sought function as a sample function of a
non-stationary Gaussian Process (GP), that nests within itself multiple other
GPs, each of which we prove can be stationary, thereby establishing sufficiency
of two GP layers. In fact, a non-stationary kernel is envisaged, with each
hyperparameter set as dependent on the sample function drawn from the outer
non-stationary GP, such that a new sample function is drawn at every pair of
input values at which the kernel is computed. However, such a model cannot be
implemented, and we substitute this by recalling that the average effect of
drawing different sample functions from a given GP is equivalent to that of
drawing a sample function from each of a set of GPs that are rendered
different, as updated during the equilibrium stage of the undertaken inference
(via MCMC). The kernel is fully non-parametric, and it suffices to learn one
hyperparameter per layer of GP, for each dimension of the input variable. We
illustrate this new learning strategy on a real dataset.

通过将函数模型为非平稳高斯过程的样本函数，学习一对变量之间的功能关系，解决可用数据的相关结构的不均匀性问题，并在其中嵌套多个高斯过程，从而建立了两个高斯过程层的充分性。

一种新的可靠且简约的学习策略，由两层高斯过程构成，以解决非均匀经验相关结构

A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of  Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures