Robust Subspace Recovery with Adversarial Outliers

04/05/2019
by   Tyler Maunu, et al.
0

We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to derive information-theoretic bounds of exact recovery. We then propose two tractable estimators: a variant of RANSAC and a simple relaxation of the theoretical estimator. The two estimators are fast to compute and achieve state-of-the-art theoretical performance in a noiseless RSR setting with adversarial outliers. The former estimator achieves better theoretical guarantees in the noiseless case, while the latter estimator is robust to small noise, and its guarantees significantly improve with non-adversarial models of outliers. We give a complete comparison of guarantees for the adversarial RSR problem, as well as a short discussion on the estimation of affine subspaces.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/02/2018

An Overview of Robust Subspace Recovery

This paper will serve as an introduction to the body of work on robust s...
research
02/07/2020

List Decodable Subspace Recovery

Learning from data in the presence of outliers is a fundamental problem ...
research
06/16/2023

Adversarially robust clustering with optimality guarantees

We consider the problem of clustering data points coming from sub-Gaussi...
research
05/31/2022

Communication-efficient distributed eigenspace estimation with arbitrary node failures

We develop an eigenspace estimation algorithm for distributed environmen...
research
03/27/2019

On the Adversarial Robustness of Multivariate Robust Estimation

In this paper, we investigate the adversarial robustness of multivariate...
research
05/30/2023

Asymptotic Characterisation of Robust Empirical Risk Minimisation Performance in the Presence of Outliers

We study robust linear regression in high-dimension, when both the dimen...
research
04/12/2019

Outlier-robust estimation of a sparse linear model using ℓ_1-penalized Huber's M-estimator

We study the problem of estimating a p-dimensional s-sparse vector in a ...

Please sign up or login with your details

Forgot password? Click here to reset