AI RESEARCH
On Unbiased Low-Rank Approximation with Minimum Distortion
arXiv CS.LG
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ArXi:2505.09647v2 Announce Type: replace-cross We describe an algorithm for sampling a low-rank random matrix $Q$ that best approximates a fixed target matrix $P\in\mathbb{C}^{n\times m}$ in the following sense: $Q$ is unbiased, i.e., $\mathbb{E}[Q] = P$; $\mathsf{rank}(Q)\leq r$; and $Q$ minimizes the expected Frobenius norm error $\mathbb{E}\|P-Q\|_F^2$. Our algorithm mirrors the solution to the efficient unbiased sparsification problem for vectors, except applied to the singular components of the matrix $P.