Thursday, April 24, 2014

Maurizio Filippone: 30th April

Pseudo-Marginal Bayesian Inference for Gaussian Processes

Statistical models where parameters have a hierarchical structure are commonly employed to flexibly model complex phenomena and to gain some insight into the functioning of the system under study.
Carrying out exact parameter inference for such models, which is key to achieve a sound quantification of uncertainty in parameter estimates and predictions, usually poses a number of computational challenges. In this talk, I will focus on Markov chain Monte Carlo (MCMC) based inference for hierarchical models involving Gaussian Process (GP) priors and non-Gaussian likelihood functions.
After discussing why MCMC is the only way to infer parameters "exactly" in general GP models and pointing out the challenges in doing so, I will present a practical and efficient alternative to popular MCMC reparameterization techniques based on the so called Pseudo-Marginal MCMC approach.
In particular, the Pseudo-Marginal MCMC approach yields samples from the exact posterior distribution over GP covariance parameters, but only requires an unbiased estimate of the analytically intractable marginal likelihood. Finally, I will present ways to construct unbiased estimates of the marginal likelihood in GP models, and conclude the talk by presenting results on several benchmark data and on a multi-class multiple-kernel classification problem with neuroimaging data.

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