Sequential Randomized Matrix Factorization for Gaussian Processes: Efficient Predictions and Hyper-parameter Optimization
Year: 2017
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
Awards: G3175784931, G8876996369
OpenAlex ID: W2768145851