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.

翻译：Gausian 过程(GPs)是适用于回归和分类问题的非对称贝叶斯模型。减轻其立方培训成本的方法之一是使用在数据子集方面受过培训的当地GP专家。特别是,专家产品模型通过可移植的产品操作将当地专家的预测分布结合起来。这些专家模型允许大规模分布计算,但其预测通常会受到平均或未经校正的不确定性量化的不稳定行为的影响。通过温和的软体加权校准预测,我们为多种专家产品模型提供了解决这些问题的解决方案,包括专家通用产品和强大的Bayesian委员会机器。此外,我们利用最佳运输文献并提出新的专家产品模型,将当地专家的预测结合起来,计算他们的Wasserstein Barycent,这可用于回归和分类。