# Uncertainty Quantification for Deep Regression using Contextualised Normalizing Flows

arXiv: https://arxiv.org/abs/2512.00835 · HTML: https://mlsanity.com/paper/2512.00835/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [Uncertainty quantification in medical image segmentation with normalizing flows](https://mlsanity.com/paper/2006.02683/) (2020)
- [Robust Uncertainty Quantification Using Conformalised Monte Carlo Prediction](https://mlsanity.com/paper/2308.09647/) (2023)
- [Optimisation of Large Wave Farms using a Multi-strategy Evolutionary Framework](https://mlsanity.com/paper/2003.09594/) (2020)

## Built on by (most cited first, 2 of 2)

- [Uncertainty-Aware Reward Modeling for Stable RLHF](https://mlsanity.com/paper/2606.19818/) (2026)
- [Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation](https://mlsanity.com/paper/2606.11865/) (2026)

## Abstract (arXiv)

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.