A generalization of the randomized singular value decomposition

Conference item

The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank approximation of a matrix using matrix-vector products with standard Gaussian vectors. Here, we generalize the theory of randomized SVD to multivariate Gaussian vectors, allowing one to incorporate prior knowledge of into the algorithm. This enables us to explore the continuous analogue of the randomized SVD for Hilbert--Schmidt (HS) operators using operator-function products with functions drawn from a Gaussian process (GP). We then construct a new covariance kernel for GPs, based on weighted Jacobi polynomials, which allows us to rapidly sample the GP and control the smoothness of the randomly generated functions. Numerical examples on matrices and HS operators demonstrate the applicability of the algorithm.

Authors: Boulle, N; Townsend, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: International Conference on Learning Representations
• Publication date: 2021-09-29
• Acceptance date: 2022-01-20
• Event title: Tenth International Conference on Learning Representations
• Event location: Virtual Event
• Event website: https://iclr.cc/Conferences/2022
• Event start date: 2022-04-25
• Event end date: 2022-04-29
• Language: English
• Keywords: low rank approximation; randomized SVD; FFR; Hilbert--Schmidt operators; Gaussian processes