`

Timezone: »

 
Poster
Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks
Jingqiu Ding · Samuel Hopkins · David Steurer

Wed Dec 09 09:00 PM -- 11:00 PM (PST) @ Poster Session 4 #1248

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.

In this work, we exhibit an estimator that works for heavy-tailed noise up to the BBP threshold that is optimal even for Gaussian noise. We give a non-asymptotic analysis of our estimator which relies only on the variance of each entry remaining constant as the size of the matrix grows: higher moments may grow arbitrarily fast or even fail to exist. Previously, it was only known how to achieve these guarantees if higher-order moments of the noises are bounded by a constant independent of the size of the matrix.

Our estimator can be evaluated in polynomial time by counting self-avoiding walks via a color coding technique. Moreover, we extend our estimator to spiked tensor models and establish analogous results.

Author Information

Jingqiu Ding (ETH Zurich)
Sam Hopkins (UC Berkeley)
David Steurer (ETH Zurich)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors