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

Sequential Randomized Matrix Factorization for Gaussian Processes: Efficient Predictions and Hyper-parameter Optimization