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

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