# A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Risk

arXiv: https://arxiv.org/abs/2608.05995 · HTML: https://mlsanity.com/paper/2608.05995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 83 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 30 of 43)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Nonparametric Uncertainty Quantification for Single Deterministic Neural Network](https://mlsanity.com/paper/2202.03101/) (2022)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms](https://mlsanity.com/paper/2004.10710/) (2020)
- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)

## Built on by (most cited first, 1 of 1)

- [Optimal Transport Dropout for Structured Predictive Uncertainty](https://mlsanity.com/paper/2609.33377/) (2026)

## Abstract (arXiv)

Reliable uncertainty estimates are critical in safety-sensitive applications. For such estimates to be useful in practice, it is crucial to understand the sources underlying a model's uncertainty, motivating the disentanglement of total uncertainty into epistemic and aleatoric uncertainty. Existing notions of uncertainty differ in the sources they capture and, consequently, in their definitions of aleatoric and epistemic uncertainty, with no universally accepted definition. We define uncertainty through sample-conditional pointwise posterior risk, which is the expected loss of a predictor under the distribution of plausible ground-truth functions given the observed sample. This definition unifies probabilistic and risk-based concepts of uncertainty. To assess state-of-the-art uncertainty disentanglement methods, we develop a framework that directly compares their estimates against ground-truth uncertainty defined primarily by posterior risk, alongside commonly used alternative uncertainty definitions. We find that Spectral-normalized Neural Gaussian Processes and Variational Latent Gaussian Processes most closely recover the ground-truth uncertainty, while most methods track posterior variance more closely than posterior risk, missing the predictors' bias. Beyond method rankings, we investigate how strongly estimated aleatoric and epistemic uncertainty are entangled and how sensitive uncertainty quality is to modeling choices, yielding practical guidance for uncertainty disentanglement. To support further method development and validation, we release 13 semi-synthetic UCI/OpenML datasets with known posteriors, enabling the computation of ground-truth uncertainty. Code and data will be made publicly available upon acceptance.