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

TL;DR

SNAP introduces a parameter-free, self-supervised framework that uses mutual agreement to robustly weigh candidates for aggregation and subspace estimation. By computing agreement weights through a normalized disagreement score and kernel functions, SNAP achieves exponential suppression of outlier influence and enables non-iterative robust computations that can outperform traditional iterative methods. The paper analyzes the properties of the resulting weights, develops SNAP models for robust aggregation and subspace estimation, and validates the approach on vector averaging and PCA, showing strong performance in high-dimensional settings. Overall, SNAP offers a broadly applicable, theory-grounded tool for robust computation that can serve as a foundation for future task-agnostic robustness techniques.

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.

Figures (5)

• Figure 1: Illustration of SNAP. Inliers have high mutual agreement and contribute strongly to the weighted consensus, while outliers contribute less. Data points are colored by their SNAP weight with $\kappa_l({\bf x})$. Note the outliers have weights near zero, highlighted in red. Left: 2D vector averaging. Weiszfeld: Geometric median of all points; SNAP $\kappa_g$, SNAP $\kappa_l$: Robust averaging using all points with SNAP weights. Distance to ground truth is in brackets. Right: PCA.
• Figure 2: Non-monotonic evolution of agreement weights under continuous point motion.
• Figure 3: Run-time (in seconds) for agreement weight computation for vectors in $\mathbb{R}^m$ and rankings of length $l$.
• Figure 4: Example results for PCA estimation, with and without SNAP weights. a): 20% outliers; b) 30% outliers; c) 40% outliers; d) 49% outliers. The result for 10% outliers is shown in Figure \ref{['fig:illustration']} (right).
• Figure 5: Moving average. Example result for Exponential Weighted Moving Average, with and without SNAP computed weights.

Theorems & Definitions (20)

• Proposition 4.1
• Proposition 4.2
• Proposition 4.3: Disagreement Monotonicity
• Proposition 4.4: Maximal Agreement Weight
• Proposition 4.5
• Proposition 4.6: restate=propSensitivity, name=Local Sensitivity Analysis
• Proposition 4.7: restate=propDisagreementSensitivity, name= Strict Disagreement Sensitivity
• Proposition 4.8: restate=propGlobalBound, name= Global Bounded Variation
• Proposition 4.9: restate=propOutlierAmplification, name= Suppression of Outlier Weights
• Theorem 4.11: restate=Suppression, name= Exponential Suppression of Outlier Weights