On Unbiased Low-Rank Approximation with Minimum Distortion
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Abstract (arXiv)
We describe an algorithm for sampling a low-rank random matrix Q that best approximates a fixed target matrix P∈mathbbCn× m in the following sense: Q is unbiased, i.e., mathbbE[Q] = P; mathsfrank(Q)≤ r; and Q minimizes the expected Frobenius norm error mathbbE|P-Q|F2. Our algorithm mirrors the solution to the efficient unbiased sparsification problem for vectors, except applied to the singular components of the matrix P. Optimality is proven by showing that our algorithm matches the error from an existing lower bound.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 7 of its 10 references that are in the map. First posted on arXiv 12 May 2025.
Builds on
7 of 10 references.
References · 7
- 2019PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimizationcited by 238
- 2018ATOMO: Communication-efficient Learning via Atomic Sparsificationcited by 136
- 2017Unbiased Online Recurrent Optimizationcited by 47
- 2019Optimal Kronecker-Sum Approximation of Real Time Recurrent Learningcited by 22
- 2015Training recurrent networks online without backtrackingcited by 10
- 2024Efficient Unbiased Sparsificationcited by 2
- 2019An unbiased approach to low rank recoverycited by 1
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Citing papers per year: 2026: 1.
1 paper.