Perturbation Analysis of Randomized SVD and its Applications to High-dimensional Statistics. (arXiv:2203.10262v2 [math.ST] UPDATED)

Randomized singular value decomposition (RSVD) is a class of computationally
efficient algorithms for computing the truncated SVD of large data matrices.
Given a $n \times n$ symmetric matrix $\mathbf{M}$, the prototypical RSVD
algorithm outputs an approximation of the $k$ leading singular vectors of
$\mathbf{M}$ by computing the SVD of $\mathbf{M}^{g} \mathbf{G}$; here $g \geq
1$ is an integer and $\mathbf{G} \in \mathbb{R}^{n \times k}$ is a random
Gaussian sketching matrix. In this paper we study the statistical properties of
RSVD …

analysis applications arxiv math statistics svd