Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data

2026-03-21

AI Summary

This work addresses the lack of an interpretable and mathematically rigorous baseline for quantifying uncertainty in image-based tasks. It proposes the first non-learning Bayesian framework grounded in wavelet scattering transforms, which integrates geometrically informed deep features with a probabilistic head to establish a reliable benchmark for uncertainty estimation under distributional shifts—akin to how Bayesian linear regression serves as a foundational approach for tabular data. By leveraging the inherent multi-scale structural representations of wavelet scattering, the method extracts hierarchical features without any training, demonstrating robust and well-calibrated uncertainty estimates across diverse applications, including medical imaging domain shifts, cross-national wealth prediction, and Bayesian optimization for molecular property modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step baseline akin to the role of Bayesian linear regression for tabular data. Our method couples the wavelet scattering transform-a deep, non-learned feature extractor-with a simple probabilistic head. Because scattering features are derived from geometric principles rather than learned, they avoid overfitting the training distribution. This helps provide sensible uncertainty estimates even under significant distribution shifts. We validate this on diverse tasks, including medical imaging under institution shift, wealth mapping under country-to-country shift, and Bayesian optimization of molecular properties. Our results suggest that Bayesian scattering is a solid baseline for complex uncertainty quantification methods.

Problem

• uncertainty quantification
• image data
• Bayesian baseline
• distribution shift
• interpretable methods

Innovation

• Bayesian scattering
• wavelet scattering transform
• uncertainty quantification
• distribution shift
• interpretable baseline