Trustworthy scientific inference for inverse problems with generative models

2025-08-04

AI Summary

In scientific inverse problems, generative models often yield biased parameter estimates or overconfident uncertainty quantification. To address this, we propose FreB—a novel framework that unifies frequentist confidence set construction with Bayesian posterior sampling, thereby establishing a mathematically rigorous, coverage-guaranteed, and interval-tight inference protocol. FreB requires no explicit likelihood evaluation, is compatible with arbitrary generative models, and incorporates interpretable diagnostic tools for uncertainty calibration. It robustly handles challenging scenarios including distributional shift, model misspecification, and observational bias. Evaluated across multiple physical science benchmarks, FreB achieves nominal coverage rates while reducing average confidence interval width by 32%–57%. To our knowledge, it is the first method offering both theoretical guarantees and practical efficacy for trustworthy scientific inference grounded in generative modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to ``inverse problems'' to infer hidden parameters from observed data. While these methods can handle intractable models and large-scale studies, they can also produce biased or overconfident conclusions. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated probability distributions into confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.

Problem

• Ensuring trustworthy inference in generative model-based inverse problems
• Addressing biased or overconfident conclusions from AI-generated distributions
• Providing validity guarantees without direct likelihood evaluation

Innovation

• Frequentist-Bayes protocol reshapes AI distributions
• Ensures confidence regions include true parameters
• Validates inference without direct likelihood evaluation