Sparse Information Filter for Fast Gaussian Process Regression

Lucas Kania, Manuel Schürch, Dario Azzimonti, Alessio Benavoli

Abstract: Gaussian processes (GPs) are an important tool in machine learning and applied mathematics with applications ranging from Bayesian optimization to calibration of computer experiments. They constitute a powerful kernelized non-parametric method with well-calibrated uncertainty estimates, however, off-the-shelf GP inference procedures are limited to datasets with a few thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques were developed over the past years. In this paper, we focus on GP regression tasks and propose a new algorithm to train variational sparse GP models. An analytical posterior update expression based on the Information Filter is derived for the variational sparse GP model. We benchmark our method on several real datasets with millions of data points against the state-of-the-art Stochastic Variational GP (SVGP) and sparse orthogonal variational inference for Gaussian Processes (SOLVEGP). Our method achieves comparable performances to SVGP and SOLVEGP while providing considerable speed-ups. Specifically, it is consistently four times faster than SVGP and on average 2.5 times faster than SOLVEGP.