Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks

Abstract

We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is to estimate the rank-1 part. For the case of Gaussian noise, the top eigenvector of the given matrix is a widely-studied estimator known to achieve optimal statistical guarantees, e.g., in the sense of the celebrated BBP phase transition. However, this estimator can fail completely for heavy-tailed noise.

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Cite

Text

Ding et al. "Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks." Neural Information Processing Systems, 2020.

Markdown

[Ding et al. "Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks." Neural Information Processing Systems, 2020.](https://mlanthology.org/neurips/2020/ding2020neurips-estimating/)

BibTeX

@inproceedings{ding2020neurips-estimating,
  title     = {{Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks}},
  author    = {Ding, Jingqiu and Hopkins, Samuel and Steurer, David},
  booktitle = {Neural Information Processing Systems},
  year      = {2020},
  url       = {https://mlanthology.org/neurips/2020/ding2020neurips-estimating/}
}