Enabling scalable stochastic gradient-based inference for Gaussian processes by employing the Unbiased LInear System SolvEr (ULISSE)

Abstract

In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the Stochastic Gradient Langevin Dynamics algorithm to draw samples from the posterior distribution over covariance parameters with negligible bias and without the need to compute the marginal likelihood. In Gaussian process regression, this has the enormous advantage that stochastic gradients can be computed by solving linear systems only. A novel unbiased linear systems solver based on parallelizable covariance matrix-vector products is developed to accelerate the unbiased estimation of gradients. The results demonstrate the possibility to enable scalable and exact (in a Monte Carlo sense) quantification of uncertainty in Gaussian processes without imposing any special structure on the covariance or reducing the number of input vectors.

10 pages - paper accepted at ICML 2015

References in corpus (6)

• Slice sampling covariance hyperparameters of latent Gaussian models
• (Non-) asymptotic properties of Stochastic Gradient Langevin Dynamics
• Consistency and fluctuations for stochastic gradient Langevin dynamics
• Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching
• Preconditioned Krylov solvers for kernel regression
• Scalable iterative methods for sampling from massive Gaussian random vectors

Cited by in corpus (4)

• Variational Fourier features for Gaussian processes
• MCMC for Variationally Sparse Gaussian Processes
• Online Sampling from Log-Concave Distributions
• Bias-Free Scalable Gaussian Processes via Randomized Truncations