Stein Variational Gaussian Processes

Abstract

We show how to use Stein variational gradient descent (SVGD) to carry out inference in Gaussian process (GP) models with non-Gaussian likelihoods and large data volumes. Markov chain Monte Carlo (MCMC) is extremely computationally intensive for these situations, but the parametric assumptions required for efficient variational inference (VI) result in incorrect inference when they encounter the multi-modal posterior distributions that are common for such models. SVGD provides a non-parametric alternative to variational inference which is substantially faster than MCMC. We prove that for GP models with Lipschitz gradients the SVGD algorithm monotonically decreases the Kullback-Leibler divergence from the sampling distribution to the true posterior. Our method is demonstrated on benchmark problems in both regression and classification, a multimodal posterior, and an air quality example with 550,134 spatiotemporal observations, showing substantial performance improvements over MCMC and VI.

26 pages, 5 figures

References in corpus (5)

• MCMC for Variationally Sparse Gaussian Processes
• Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling
• A Non-Asymptotic Analysis for Stein Variational Gradient Descent
• Convergence of Sparse Variational Inference in Gaussian Processes Regression
• The equivalence between Stein variational gradient descent and black-box variational inference

Cited by in corpus (2)

• A Probabilistic Assessment of the COVID-19 Lockdown on Air Quality in the UK
• Gaussian Processes on Hypergraphs