Gaussian Processes Over Graphs

Gaussian processes are a natural extension of the ubiquitous kernel regression to the Bayesian setting where the regression parameters are modelled as random variables with a Gaussian prior distribution [1]. Given the training observations, Gaussian processes generate posterior probabilities of the target or output for new inputs or observations, as a function of the training data and the input kernel function [2]. Gaussian process models and its variants have been applied in a number of diverse fields such as model predictive control and system analysis [3]-[7], latent variable models [8]-[11], multi-task learning [10], [12], [13], image analysis and synthesis [14]- [17], speech processing [18]-[20], and magnetic resonance imaging (MRI) [21], [22]. Gaussian processes have also been extended to a non-stationary regression setting [23]-[25] and for regression over complex-valued data [26]. Recently, Gaussian processes were shown to be useful in training and analysis of deep neural networks, and that a Gaussian process can be viewed as a neural network with a single infinite-dimensional layer of hidden units [27], [28].