Healing Products of Gaussian Processes
This work addresses a specific bottleneck in scalable Gaussian process modeling for practitioners, offering incremental improvements to existing methods.
The paper tackles the erratic predictions and uncalibrated uncertainties in product-of-expert Gaussian process models by introducing a tempered softmax weighting for calibration and a new model based on Wasserstein barycenters, achieving improved performance in regression and classification tasks.
Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.