Many statistical learning methodologies exhibit loss of efficiency and accuracy when applied to large, high-dimensional data-sets. Such loss is exacerbated by noisy data. In this paper, we focus on Gaussian Processes (GPs), a family of non-parametric approaches used in machine learning and Bayesian Optimization. In fact, GPs show difficulty scaling with the input data size and dimensionality. This paper presents, for the first time, the Stochastic GP Model Averaging (SGPMA) algorithm, to tackle both challenges. SGPMA uses a Bayesian approach to weight several predictors, each trained with an independent subset of the initial data-set (solving the large data-sets issue), and defined in a low-dimensional embedding of the original space (solving the high dimensionality). We conduct several experiments with different input size and dimensionality. The results show that our methodology is superior to naive averaging and that the embedding choice is critical to manage the computational cost / prediction accuracy trade-off.