4 research outputs found
Enabling scalable stochastic gradient-based inference for Gaussian processes by employing the Unbiased LInear System SolvEr (ULISSE)
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.Comment: 10 pages - paper accepted at ICML 201
Adaptive Multiple Importance Sampling for Gaussian Processes
In applications of Gaussian processes where quantification of uncertainty is
a strict requirement, it is necessary to accurately characterize the posterior
distribution over Gaussian process covariance parameters. Normally, this is
done by means of standard Markov chain Monte Carlo (MCMC) algorithms. Motivated
by the issues related to the complexity of calculating the marginal likelihood
that can make MCMC algorithms inefficient, this paper develops an alternative
inference framework based on Adaptive Multiple Importance Sampling (AMIS). This
paper studies the application of AMIS in the case of a Gaussian likelihood, and
proposes the Pseudo-Marginal AMIS for non-Gaussian likelihoods, where the
marginal likelihood is unbiasedly estimated. The results suggest that the
proposed framework outperforms MCMC-based inference of covariance parameters in
a wide range of scenarios and remains competitive for moderately large
dimensional parameter spaces.Comment: 27 page