Student-t processes as alternatives to Gaussian processes

Amar Shah, Andrew Gordon Wilson, Zoubin Ghahramani

Research output: Contribution to journalConference articlepeer-review


We investigate the Student-t process as an alternative to the Gaussian process as a non-parametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the co-variance kernel of a Gaussian process model. We show surprising equivalences between different hierarchical Gaussian process models leading to Student-t processes, and derive a new sampling scheme for the inverse Wishart process, which helps elucidate these equivalences. Overall, we show that a Student-t process can retain the attractive properties of a Gaussian process - a nonparamet-ric representation, analytic marginal and predictive distributions, and easy model selection through covariance kernels - but has enhanced flexibility, and predictive covariances that, unlike a Gaussian process, explicitly depend on the values of training observations. We verify empirically that a Student-t process is especially useful in situations where there are changes in covariance structure, or in applications such as Bayesian optimization, where accurate predictive covariances are critical for good performance. These advantages come at no additional computational cost over Gaussian processes.

Original languageEnglish (US)
Pages (from-to)877-885
Number of pages9
JournalJournal of Machine Learning Research
StatePublished - 2014
Event17th International Conference on Artificial Intelligence and Statistics, AISTATS 2014 - Reykjavik, Iceland
Duration: Apr 22 2014Apr 25 2014

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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