Enabling scalable stochastic gradient-based inference for Gaussian processes by employing the Unbiased LInear System SolvEr (ULISSE)
This enables scalable and exact uncertainty quantification for Gaussian processes, addressing a bottleneck in applications where uncertainty is critical, though it is incremental as it builds on existing stochastic gradient methods.
The paper tackles the problem of scalable uncertainty quantification in Gaussian processes by adapting Stochastic Gradient Langevin Dynamics to sample from the posterior distribution over covariance parameters without computing the marginal likelihood, using a novel unbiased linear systems solver to accelerate gradient estimation, achieving exact Monte Carlo inference without structural constraints.
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.