Name
Title | ||
|---|---|---|
Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing |
Abstract | ||
|---|---|---|
We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our first robust PCA algorithm runs in polynomial time, returns a $1 - O(\epsilon\log\epsilon^{-1})$-approximate top eigenvector, and is based on a simple iterative filtering approach. Our second, which attains a slightly worse approximation factor, runs in nearly-linear time and sample complexity under a mild spectral gap assumption. These are the first polynomial-time algorithms yielding non-trivial information about the covariance of a corrupted sub-Gaussian distribution without requiring additional algebraic structure of moments. As a key technical tool, we develop the first width-independent solvers for Schatten-$p$ norm packing semidefinite programs, giving a $(1 + \epsilon)$-approximate solution in $O(p\log(\tfrac{nd}{\epsilon})\epsilon^{-1})$ input-sparsity time iterations (where $n$, $d$ are problem dimensions). |
Year | Venue | DocType |
|---|---|---|
2020 | NIPS 2020 | Conference |
Volume | Citations | PageRank |
33 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arun Jambulapati | 1 | 1 | 2.05 |
| Jerry Li | 2 | 229 | 22.67 |
| Kevin Tian | 3 | 3 | 6.47 |