Ribbon: Scalable Approximation and Robust Uncertainty Quantification

2026-06-25

AI Summary

Quantifying predictive uncertainty remains challenging in complex, high-dimensional, or misspecified models. This work proposes Ribbon, a method that leverages influence functions to linearize and approximate Dirichlet reweighting bootstrap, thereby transforming the Bayesian bootstrap’s reweighting mechanism into a lightweight post-processing step requiring only a single model training. By integrating Laplace approximation with sandwich covariance estimation and enabling uncertainty scale calibration using validation data, Ribbon avoids the computational burden of repeated retraining. Empirical evaluations on synthetic regression, MNIST classification, and California housing datasets demonstrate that Ribbon achieves predictive performance comparable to existing approaches while substantially improving uncertainty calibration.

Abstract

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for modern machine-learning models because they require posterior sampling or repeated model refitting. We introduce Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty. Ribbon replaces repeated refitting with an influence-function linearization around a single fitted model, preserving the first-order data-reweighting structure of the Bayesian bootstrap while requiring only post-hoc linear algebra. Ribbon approximates the Bayesian-bootstrap or weighted-likelihood-bootstrap refitting target. With a general concentration parameter, Ribbon gives a calibrated Dirichlet-reweighting family whose uncertainty scale can be tuned on validation data. We show that Ribbon is asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification and recovers the robust sandwich covariance under misspecification. Across synthetic regression, MNIST classification, and California Housing benchmarks, Ribbon provides competitive predictive performance and improved calibration in several settings while avoiding repeated model retraining.

Problem

• uncertainty quantification
• scalable approximation
• Bayesian bootstrap
• model misspecification
• predictive uncertainty

Innovation

• uncertainty quantification
• scalable approximation
• influence function
• Dirichlet reweighting
• Bayesian bootstrap