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

TL;DR

SNAP is a self-supervised framework that enhances robust computation by assigning weights based on mutual agreement, effectively suppressing outliers even in high-dimensional data.

Contribution

The paper introduces SNAP, a novel self-supervised agreement-based method that outperforms existing algorithms in robust vector averaging and subspace estimation.

Findings

Outliers are exponentially suppressed in high-dimensional settings.

Non-iterative SNAP outperforms iterative algorithms like Weiszfeld.

SNAP provides a flexible and broadly applicable robust computation approach.

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.