Miguel Lázaro-Gredilla, Aníbal Figueiras-Vidal
We present a general inference framework for inter-domain Gaussian Processes (GPs), focusing on its usefulness to build sparse GP models. The state-of-the-art sparse GP model introduced by Snelson and Ghahramani in  relies on finding a small, representative pseudo data set of m elements (from the same domain as the n available data elements) which is able to explain existing data well, and then uses it to perform inference. This reduces inference and model selection computation time from O(n^3) to O(m^2n), where m << n. Inter-domain GPs can be used to find a (possibly more compact) representative set of features lying in a different domain, at the same computational cost. Being able to specify a different domain for the representative features allows to incorporate prior knowledge about relevant characteristics of data and detaches the functional form of the covariance and basis functions. We will show how previously existing models fit into this framework and will use it to develop two new sparse GP models. Tests on large, representative regression data sets suggest that significant improvement can be achieved, while retaining computational efficiency.