Reproduce “Mixtures of Gaussian Processes for regression under multiple prior distributions” on OpenResearch

About this paper

Sarem Seitz

A framework utilizing Mixtures of Gaussian Processes (MGPs) is introduced for aggregating multiple functional prior distributions, demonstrating improved robustness against prior misspecification and enhanced data efficiency for extrapolation by incorporating a flexible 'catch-all' prior and supporting scalable inference.

Key insights

• Theoretical proof of existence and fundamental properties (marginalization, conditioning) for linearly-pooled MGPs, formally defining them as a consistent stochastic process.
• Derivation of an analytical posterior predictive distribution for plain MGPs, where the posterior mixture weights are dynamically updated based on how well each individual GP component explains the observed data.
• Establishment of a scalable SV-MGP with a closed-form ELBO that enables efficient variational inference over inducing points for each component and the mixture coefficients, making the approach practical for larger datasets.

Summary by alphaXiv.