Uncertainty Quantification for Deep Regression using Contextualised Normalizing Flows

2025-11-30

AI Summary

Quantifying uncertainty in deep regression models is critical for high-stakes decision-making, yet existing approaches either produce only prediction intervals—ignoring distributional shape—or rely on Bayesian retraining, which is computationally prohibitive. This paper proposes a post-hoc, training-free framework that introduces Contextualized Normalizing Flows (CNFs), a novel class of conditional normalizing flows conditioned on pre-trained model outputs to directly estimate the full conditional predictive distribution. CNFs flexibly capture complex distributional characteristics—including multimodality and asymmetry—while simultaneously yielding well-calibrated prediction intervals and complete probability density estimates. Extensive experiments demonstrate that our method achieves uncertainty estimation quality on par with state-of-the-art approaches, significantly enhancing both reliability and informativeness of downstream decisions without requiring model retraining or architectural modification.

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 learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Quantifies uncertainty in deep regression models for safe decision-making.
• Addresses limitations of existing methods that overlook distributional information.
• Introduces a post hoc method without needing model retraining.

Innovation

• Post hoc method using contextualised normalizing flows
• Generates prediction intervals and full predictive distributions
• No retraining needed for underlying predictive model