Rapid Uncertainty Computation with Gaussian Processes and Histogram Intersection Kernels

Abstract

An important advantage of Gaussian processes is the ability to directly estimate classification uncertainties in a Bayesian manner. In this paper, we develop techniques that allow for estimating these uncertainties with a runtime linear or even constant with respect to the number of training examples. Our approach makes use of all training data without any sparse approximation technique while needing only a linear amount of memory. To incorporate new information over time, we further derive online learning methods leading to significant speed-ups and allowing for hyperparameter optimization on-the-fly. We conduct several experiments on public image datasets for the tasks of one-class classification and active learning, where computing the uncertainty is an essential task. The experimental results highlight that we are able to compute classification uncertainties within microseconds even for large-scale datasets with tens of thousands of training examples.