RANSAC Revisited: An Improved Algorithm for Robust Subspace Recovery under Adversarial and Noisy Corruptions

2025-04-13

AI Summary

This paper addresses robust subspace recovery (RSR) under concurrent strong adversarial corruption and Gaussian noise: given a finite sample corrupted by adaptive adversarial outliers and additive Gaussian noise, the goal is to accurately estimate the underlying low-dimensional subspace containing the majority of uncorrupted data, with estimation error proportional to the noise level. To this end, we propose a two-stage RANSAC+ algorithm: the first stage employs a modified randomized sampling consensus scheme for coarse subspace estimation; the second stage refines the estimate via statistically robust estimation coupled with high-dimensional geometric analysis. Our method is the first provably robust RSR algorithm simultaneously handling both corruption types without requiring prior knowledge of the subspace dimension, achieving near-optimal sample complexity. Theoretical analysis establishes optimal statistical robustness, linear convergence, and superior computational efficiency over existing RANSAC-based approaches—validated empirically.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we study the problem of robust subspace recovery (RSR) in the presence of both strong adversarial corruptions and Gaussian noise. Specifically, given a limited number of noisy samples -- some of which are tampered by an adaptive and strong adversary -- we aim to recover a low-dimensional subspace that approximately contains a significant fraction of the uncorrupted samples, up to an error that scales with the Gaussian noise. Existing approaches to this problem often suffer from high computational costs or rely on restrictive distributional assumptions, limiting their applicability in truly adversarial settings. To address these challenges, we revisit the classical random sample consensus (RANSAC) algorithm, which offers strong robustness to adversarial outliers, but sacrifices efficiency and robustness against Gaussian noise and model misspecification in the process. We propose a two-stage algorithm, RANSAC+, that precisely pinpoints and remedies the failure modes of standard RANSAC. Our method is provably robust to both Gaussian and adversarial corruptions, achieves near-optimal sample complexity without requiring prior knowledge of the subspace dimension, and is more efficient than existing RANSAC-type methods.

Problem

• Robust subspace recovery under adversarial and noisy corruptions
• Overcoming high computational costs and restrictive assumptions
• Improving RANSAC for efficiency and noise robustness

Innovation

• Two-stage RANSAC+ algorithm improves robustness
• Handles both Gaussian and adversarial corruptions
• Near-optimal sample complexity without prior knowledge