Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models

TL;DR

This paper explores how Gaussian Process models can be used to separate derivatives, uncertainty, and error in Earth observation data, enhancing temperature prediction accuracy by analyzing predictive variance and error propagation.

Contribution

It introduces an analytical error propagation method using GP derivatives, specifically addressing input noise in geoscience applications.

Findings

GP derivatives enable analytical error propagation.

Analysis of predictive variance improves temperature prediction.

Method enhances understanding of uncertainty in Earth observation models.

Abstract

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually available. In this paper, we showcase how the derivative of a GP model can be used to provide an analytical error propagation formulation and we analyze the predictive variance and the propagated error terms in a temperature prediction problem from infrared sounding data.