Log In Sign Up

Accounting for Input Noise in Gaussian Process Parameter Retrieval

by   J. Emmanuel Johnson, et al.

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data.


page 5

page 6

page 7


Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models

Gaussian Processes (GPs) are a class of kernel methods that have shown t...

Learning Structures in Earth Observation Data with Gaussian Processes

Gaussian Processes (GPs) has experienced tremendous success in geoscienc...

Physics-Aware Gaussian Processes in Remote Sensing

Earth observation from satellite sensory data poses challenging problems...

Multi-class Gaussian Process Classification with Noisy Inputs

It is a common practice in the supervised machine learning community to ...

Joint Gaussian Processes for Biophysical Parameter Retrieval

Solving inverse problems is central to geosciences and remote sensing. R...

Fully-probabilistic Terrain Modelling with Stochastic Variational Gaussian Process Maps

Gaussian processes (GPs) are becoming a standard tool to build terrain r...

Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes

Nonlinear model predictive control (NMPC) is an efficient approach for t...