A1337
Title: Vecchia-inducing-points full-scale approximations for Gaussian processes
Authors: Tim Gyger - Lucerne University of Applied Sciences (Switzerland) [presenting]
Fabio Sigrist - ETH Zurich (Switzerland)
Reinhard Furrer - University of Zurich (Switzerland)
Abstract: Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, Vecchia-inducing-points full-scale (VIF) approximations are proposed, combining the strengths of global inducing points and local Vecchia approximations. Vecchia approximations excel in settings with low-dimensional inputs and moderately smooth covariance functions, while inducing point methods are better suited to high-dimensional inputs and smoother covariance functions. The VIF approach bridges these two regimes by using an efficient correlation-based neighbor-finding strategy for the Vecchia approximation of the residual process, implemented via a modified cover tree algorithm. The framework is further extended to non-Gaussian likelihoods by introducing iterative methods that substantially reduce computational costs for training and prediction by several orders of magnitude compared to Cholesky-based computations when using a Laplace approximation. In particular, novel preconditioners are proposed and compared, and theoretical convergence results are provided. Extensive numerical experiments on simulated and real-world data sets show that VIF approximations are both computationally efficient, as well as more accurate and numerically stable than state-of-the-art alternatives.
