  This paper presents a sequential randomized lowrank matrix factorization
approach for incrementally predicting values of an unknown function at test
points using the Gaussian Processes framework. It is well-known that in the
Gaussian processes framework, the computational bottlenecks are the inversion
of the (regularized) kernel matrix and the computation of the hyper-parameters
defining the kernel. The main contributions of this paper are two-fold. First,
we formalize an approach to compute the inverse of the kernel matrix using
randomized matrix factorization algorithms in a streaming scenario, i.e., data
is generated incrementally over time. The metrics of accuracy and computational
efficiency of the proposed method are compared against a batch approach based
on use of randomized matrix factorization and an existing streaming approach
based on approximating the Gaussian process by a finite set of basis vectors.
Second, we extend the sequential factorization approach to a class of kernel
functions for which the hyperparameters can be efficiently optimized. All
results are demonstrated on two publicly available datasets.
