Adaptive multiple importance sampling for Gaussian processes

0469804 - ÚTIA 2018 RIV GB eng J - Journal Article
Xiong, X. - Šmídl, Václav - Filippone, M.
Adaptive multiple importance sampling for Gaussian processes.
Journal of Statistical Computation and Simulation. Roč. 87, č. 8 (2017), s. 1644-1665. ISSN 0094-9655. E-ISSN 1563-5163
R&D Projects: GA MŠMT(CZ) 7F14287
Institutional support: RVO:67985556
Keywords : Gaussian Process * Bayesian estimation * Adaptive importance sampling
OECD category: Statistics and probability
Impact factor: 0.869, year: 2017
http://library.utia.cas.cz/separaty/2017/AS/smidl-0469804.pdf

In applications of Gaussian processes (GPs) where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. This is normally done by means of standard Markov chain Monte Carlo (MCMC) algorithms, which require repeated expensive calculations involving the marginal likelihood. Motivated by the desire to avoid the inefficiencies of MCMC algorithms rejecting a considerable amount of expensive proposals, this paper develops an alternative inference framework based on adaptive multiple importance sampling (AMIS). In particular, this paper studies the application of AMIS for GPs in the case of a Gaussian likelihood, and proposes a novel pseudo-marginal-based AMIS algorithm 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.
Permanent Link: http://hdl.handle.net/11104/0270731