SNAP: A Self-Consistent Agreement Principle with Application to Robust Computation

2026-02-02

AI Summary

This work proposes SNAP, a robust framework for high-dimensional unsupervised settings where outliers severely degrade performance. Built upon the principle of self-consistency, SNAP introduces a mutual consistency measure that assigns reliability weights to data samples without requiring any prior knowledge. The method incorporates an exponential suppression mechanism to achieve non-iterative, unsupervised robust estimation, making it suitable for tasks such as vector averaging and subspace estimation. Under the Agreement-Reliability assumption, SNAP employs a self-supervised consistency-weighting strategy that effectively amplifies trustworthy samples while suppressing outliers. Extensive experiments demonstrate that SNAP consistently outperforms the Weiszfeld algorithm and variants of the multivariate median across multiple high-dimensional tasks, exhibiting superior robustness and practical utility.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and 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
• Security and Privacy: Large-scale security measurements

Abstract

We introduce SNAP (Self-coNsistent Agreement Principle), a self-supervised framework for robust computation based on mutual agreement. Based on an Agreement-Reliability Hypothesis SNAP assigns weights that quantify agreement, emphasizing trustworthy items and downweighting outliers without supervision or prior knowledge. A key result is the Exponential Suppression of Outlier Weights, ensuring that outliers contribute negligibly to computations, even in high-dimensional settings. We study properties of SNAP weighting scheme and show its practical benefits on vector averaging and subspace estimation. Particularly, we demonstrate that non-iterative SNAP outperforms the iterative Weiszfeld algorithm and two variants of multivariate median of means. SNAP thus provides a flexible, easy-to-use, broadly applicable approach to robust computation.

Problem

• robust computation
• outlier suppression
• self-supervised learning
• high-dimensional statistics
• vector averaging

Innovation

• Self-supervised robust computation
• Self-consistent agreement
• Exponential suppression of outliers
• Weighted consensus
• Non-iterative robust estimation