Fast Allocation of Gaussian Process Experts

We propose a scalable nonparametric Bayesian regression model based on a mixture of Gaussian process (GP) experts and the inducing points formalism underpinning sparse GP approximations. Each expert is augmented with a set of inducing points, and the allocation of data points to experts is defined probabilistically based on their proximity to the experts. This allocation mechanism enables a fast variational inference procedure for learning of the inducing inputs and hyperparameters of the experts. When using K experts, our method can run K^2 times faster and use K^2 times less memory than popular sparse methods such as the FITC approximation. Furthermore, it is easy to parallelize and handles non-stationarity straightforwardly. Our experiments show that on medium-sized datasets (of around 10^4 training points) it trains up to 5 times faster than FITC while achieving comparable accuracy. On a large dataset of 10^5 training points, our method significantly outperforms six competitive baselines while requiring only a few hours of training.