Gaussian Process Sensitivity Analysis for Oceanic Chlorophyll Estimation

Abstract

Gaussian process regression (GPR) has experienced tremendous success in biophysical parameter retrieval in the past years. The GPR provides a full posterior predictive distribution so one can derive mean and variance predictive estimates, i.e., point-wise predictions and associated confidence intervals. GPR typically uses translation invariant covariances that make the prediction function very flexible and nonlinear. This, however, makes the relative relevance of the input features hardly accessible, unlike in linear prediction models. In this paper, we introduce the sensitivity analysis of the GPR predictive mean and variance functions to derive feature rankings and spectral spacings, respectively. The methodology can be used to uncover knowledge in any kernel-based regression method, it is fast to compute, and it is expressed in closed-form. The methodology is evaluated on GPR for global ocean chlorophyll prediction, revealing the most important spectral bands and their spectral spacings. We illustrate the (successful) methodology in several datasets and sensors.