Sequential randomized matrix factorization for Gaussian processes

The Gaussian process framework models a function as a stochastic process such that the training data results into a finite number of jointly Gaussian random variables, whose properties can then be used to infer the statistics (the mean and variance) of the function at test values for the input. The computation can be implemented in a batch setting, i.e., one-shot over the entire training data, or in a sequential setting where the data is processed incrementally. In either setting, the scalability of the computation grows with the number of points in the (training) data. This paper addresses the scalability aspect of Gaussian processes in sequential settings using recent advances in randomized matrix computations.