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Sparse Gaussian Process Hyperparameters: Optimize or Integrate?
Vidhi Lalchand · Wessel Bruinsma · David Burt · Carl Edward Rasmussen

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #433

The kernel function and its hyperparameters are the central model selection choice in a Gaussian process (Rasmussen and Williams, 2006).Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an approach known as Type-II maximum likelihood (ML-II). However, ML-II does not account for hyperparameter uncertainty, and it is well-known that this can lead to severely biased estimates and an underestimation of predictive uncertainty. While there are several works which employ fully Bayesian characterisation of GPs, relatively few propose such approaches for the sparse GPs paradigm. In this work we propose an algorithm for sparse Gaussian process regression which leverages MCMC to sample from the hyperparameter posterior within the variational inducing point framework of (Titsias, 2009). This work is closely related to (Hensman et al, 2015b) but side-steps the need to sample the inducing points, thereby significantly improving sampling efficiency in the Gaussian likelihood case. We compare this scheme against natural baselines in literature along with stochastic variational GPs (SVGPs) along with an extensive computational analysis.

Author Information

Vidhi Lalchand (University of Cambridge)

Ph.D student in Machine learning at Cambridge, I work on Bayesian Non-parametrics, Gaussian Processes, Kernel Learning. Application Areas: High Energy Physics, Astronomy, Science!

Wessel Bruinsma (Microsoft Research AI4Science)
David Burt (Massachusetts Institute of Technology)
Carl Edward Rasmussen (University of Cambridge)

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