SNAP: A Self-Consistent Agreement Principle with Application to Robust Computation
This provides a flexible and broadly applicable approach to robust computation, addressing issues with outliers in high-dimensional settings, though it appears incremental as it builds on existing robust computation principles.
The paper tackles the problem of robust computation by introducing SNAP, a self-supervised framework that uses mutual agreement to weight trustworthy items and suppress outliers, demonstrating that it outperforms existing methods like the Weiszfeld algorithm and multivariate median of means variants.
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.