Active Learning for Gaussian Processes Based on Global Sensitivity Analysis

Gaussian processes (GPs) are a powerful method for modeling complex systems, providing predictions along with uncertainties. Learning surrogate models requires experiments, which are often costly or time-consuming. Keeping the number of experiments small through careful acquisition is desirable for computational and resource efficiency. Active learning (AL) has been shown to achieve better generalization with a limited number of training samples while keeping the number of queries small. In the field of machine learning (ML), sensitivity analysis (SA) plays a critical role in estimating the impact of model inputs on individual outputs, enabling parameter identification and model improvement. While traditional methods of SA on GPs focus on evaluating the mean of the model prediction, the uncertainty embodied in the standard deviation of the GP output is often neglected. The sensitivity of the GP uncertainty provides an opportunity to selectively improve the model quality with a minimum of additional experiments by identifying coordinates in the input parameter space that are most sensitive to the training space. This paper presents a novel algorithm that uses Sobol indices to assess the sensitivity of the GP standard deviation, thus facilitating a novel AL method for targeted reduction of model uncertainty.