NeurIPS 2020spotlight9 citations
Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks
Jingqiu Ding, Samuel Hopkins, David Steurer
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.
BibTeX
@inproceedings{NEURIPS2020_3c0de3fe,
author = {Ding, Jingqiu and Hopkins, Samuel and Steurer, David},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
pages = {5576--5586},
publisher = {Curran Associates, Inc.},
title = {Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks},
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/3c0de3fec9ab8a3df01109251f137119-Paper.pdf},
volume = {33},
year = {2020}
}