Botond Tibor Szabo, Università Bocconi, Italy
Gaussian processes (GP) are frequently used in Bayesian nonparametrics as a prior distribution on infinite dimensional functional parameters. However, even in case of the simple nonparametric regression model with Gaussian noise the computational time scales cubically with the sample size making them impractical for large data sets. In practice several approximation methods were proposed to speed up the computations, but typically they have some tunning parameters which were chosen so far in ad hoc way. We derive theoretical guarantees and limitations of these procedures and based on our theoretical results provide the optimal choice for these tunning parameters. We demonstrate the practical performance of these approaches on numerical and real data examples. The considered approaches include: distributed GP, variational GP (inducing variable method), iterative algorithms (Lanczos and Conjugate gradient methods) and Vecchia approximation. The talk is based on joint works with: Dennis Nieman (VU Amsterdam), Thibault Randrianarisoa (Bocconi), Bernhard Stankewitz (Bocconi), Aad van der Vaart (Delft), Harry van Zanten (VU Amsterdam), Yichen Zhu (Bocconi).
