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Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data

Bernardo Fichera, Zarko Ivkovic, Kjell Jorner, Philipp Hennig, Viacheslav Borovitskiy

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.

Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data

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.
Paper Structure (55 sections, 7 equations, 4 figures, 3 tables)

This paper contains 55 sections, 7 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Uncertainty for images.
  4. Scattering transforms and applications.
  5. Scattering
  6. Defining Properties of Scattering Transforms
  7. Explicit Construction
  8. Wavelets
  9. Translation-invariant scattering transform
  10. Windowed scattering transform
  11. Rotation Invariance
  12. Feature Map Dimensionality
  13. Bayesian Scattering
  14. General Framework
  15. Instantiating the Framework
  16. ...and 40 more sections

Figures (4)

  • Figure 2: Different types of transformations that feature maps should be invariant or stable to. Note: while single steps in (\ref{['fig:transforms:deformation']}) are small deformations, their composition changes the image content.
  • Figure 3: Datasets used in \ref{['sec:experiments']} with the exception of QM9 whose 3D image representations are difficult to visualize.
  • Figure 4: Regret of BO of molecular properties. Curves show the mean over 5 runs; shaded regions show $0.95$ confidence intervals. In the legend, RS stands for random search, UMOL for Uni-Mol, BS for Bayesian scattering and RI for rotation-invariant.
  • Figure 5: Molecular property BO (extended). Curves show the mean regret over 5 runs; shaded regions show $0.95$ confidence intervals.