Ecole d'ingénieur et centre de recherche en Sciences du numérique

Adaptive multiple importance sampling for Gaussian processes

Xiong, Xiaoyu; Smídl, Václav; Filippone, Maurizio

Submitted on 5 August 2015 (v1), last revised 31 Mar 2016

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.

Document Arxiv Bibtex

Titre:Adaptive multiple importance sampling for Gaussian processes
Mots Clés:Gaussian processes · Bayesian inference · Markov chain Monte Carlo · Importance sampling
Département:Data Science
Eurecom ref:4875
Copyright: © EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Submitted on 5 August 2015 (v1), last revised 31 Mar 2016 and is available at :
Bibtex: @techreport{EURECOM+4875, year = {2016}, title = {{A}daptive multiple importance sampling for {G}aussian processes}, author = {{X}iong, {X}iaoyu and {S}m{\'i}dl, {V}{\'a}clav and {F}ilippone, {M}aurizio}, number = {EURECOM+4875}, month = {03}, institution = {Eurecom}, url = {},, }
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