Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements

2025-10-31

AI Summary

Objective evaluation of Bayesian imaging models remains challenging in no-ground-truth scenarios, where ground-truth labels are unavailable and prior or likelihood misspecification is common. Method: This paper proposes an unsupervised evaluation framework integrating Bayesian cross-validation with data splitting—first enabling consistent assessment of implicit priors (e.g., diffusion models, deep priors) and plug-and-play samplers. It leverages multiple probabilistic scoring rules to support model selection and misspecification diagnosis while substantially reducing computational overhead compared to conventional Bayesian validation. Contribution/Results: Experiments across diverse settings—including prior misspecification, likelihood mismatch, and noise corruption—demonstrate that the method achieves significantly higher model selection accuracy and misspecification detection rates than existing baselines, with up to one-order-of-magnitude improvement in computational efficiency. The framework establishes a scalable, plug-and-play paradigm for trustworthy Bayesian inference in complex imaging inverse problems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

Problem

• Evaluating Bayesian imaging models without ground truth data
• Detecting model misspecification in imaging inverse problems
• Selecting optimal models using noisy partial measurements efficiently

Innovation

• Bayesian cross-validation combined with data fission
• Unsupervised model selection without ground truth
• Compatible with diffusion and plug-and-play samplers