Corpus ID: 11246489

Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds

@article{Zhang2015DistributedEO,
  title={Distributed Estimation of Generalized Matrix Rank: Efficient Algorithms and Lower Bounds},
  author={Yuchen Zhang and M. Wainwright and Michael I. Jordan},
  journal={ArXiv},
  year={2015},
  volume={abs/1502.01403}
}
We study the following generalized matrix rank estimation problem: given an n × n matrix and a constant c ≥ 0, estimate the number of eigenvalues that are greater than c. In the distributed setting, the matrix of interest is the sum of m matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate Ω(n2) bits, which is order equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only e O… Expand
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