Uncertainty Quantification for Deep Regression using Contextualised Normalizing Flows

2025/11/30 by Marco, Adriel Sosa, John D. Kirwan, Kirwan, John Daniel +4
Computer Science · #Adversarial Robustness in Machine Learning #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2512.00835

openalex publication_date 2025/11/30 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making. Similarly, full or approximated Bayesian methods, while yielding the predictive posterior density, demand major modifications to the model architecture and retraining. We introduce MCNF, a novel post hoc uncertainty quantification method that produces both prediction intervals and the full conditioned predictive distribution. MCNF operates on top of the underlying trained predictive model; thus, no predictive model retraining is needed. We provide experimental evidence that the MCNF-based uncertainty estimate is well calibrated, is competitive with state-of-the-art uncertainty quantification methods, and provides richer information for downstream decision-making tasks.

Citations

• Robust Uncertainty Quantification Using Conformalised Monte Carlo Prediction
• A Survey of Uncertainty in Deep Neural Networks
• Uncertainty Sets for Image Classifiers using Conformal Prediction
• Uncertainty quantification in medical image segmentation with normalizing flows
• Neural Spline Flows
• Conformalized Quantile Regression
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• Variational Dropout and the Local Reparameterization Trick
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• Regression Quantiles

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• Uncertainty-Aware (UNA) Bases for Deep Bayesian Regression Using Multi-Headed Auxiliary Networks