Pseudo-marginal Bayesian inference for Gaussian processes

Maurizio Filippone*, Mark Girolami

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


The main challenges that arise when adopting Gaussian process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion.

Original languageEnglish (US)
Article number6786502
Pages (from-to)2214-2226
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number11
StatePublished - Nov 1 2014

Bibliographical note

Publisher Copyright:
© 1979-2012 IEEE.


  • approximate Bayesian inference
  • Gaussian processes
  • Hierarchic Bayesian models
  • Kernel methods
  • Markov chain Monte Carlo
  • pseudo-marginal Monte Carlo

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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