# Post-hoc Uncertainty Learning using a Dirichlet Meta-Model

arXiv: https://arxiv.org/abs/2212.07359 · HTML: https://mlsanity.com/paper/2212.07359/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 25 of 25)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Robust Out-of-distribution Detection for Neural Networks](https://mlsanity.com/paper/2003.09711/) (2020)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Towards Maximizing the Representation Gap between In-Domain & Out-of-Distribution Examples](https://mlsanity.com/paper/2010.10474/) (2020)
- [Uncertainty Estimation Using a Single Deep Deterministic Neural Network](https://mlsanity.com/paper/2003.02037/) (2020)
- [Being Bayesian about Categorical Probability](https://mlsanity.com/paper/2002.07965/) (2020)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [Learnable Uncertainty under Laplace Approximations](https://mlsanity.com/paper/2010.02720/) (2020)
- [Confidence Scoring Using Whitebox Meta-models with Linear Classifier Probes](https://mlsanity.com/paper/1805.05396/) (2018)
- [Learning Prediction Intervals for Model Performance](https://mlsanity.com/paper/2012.08625/) (2020)

## Built on by (most cited first, 30 of 31)

- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Think Twice Before Selection: Federated Evidential Active Learning for Medical Image Analysis with Domain Shifts](https://mlsanity.com/paper/2312.02567/) (2023)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?](https://mlsanity.com/paper/2402.06160/) (2024)
- [How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networks](https://mlsanity.com/paper/2305.15508/) (2023)
- [Uncertainty-aware Language Modeling for Selective Question Answering](https://mlsanity.com/paper/2311.15451/) (2023)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Post-hoc Probabilistic Vision-Language Models](https://mlsanity.com/paper/2412.06014/) (2024)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.08766/) (2024)
- [A Confidence-based Acquisition Model for Self-supervised Active Learning and Label Correction](https://mlsanity.com/paper/2310.08944/) (2023)
- [Bi-directional Model Cascading with Proxy Confidence](https://mlsanity.com/paper/2504.19391/) (2025)
- [SurvUnc: A Meta-Model Based Uncertainty Quantification Framework for Survival Analysis](https://mlsanity.com/paper/2505.14803/) (2025)
- [Robust Adversarial Quantification via Conflict-Aware Evidential Deep Learning](https://mlsanity.com/paper/2506.05937/) (2025)
- [Evidential Transformation Network: Turning Pretrained Models into Evidential Models for Post-hoc Uncertainty Estimation](https://mlsanity.com/paper/2604.08627/) (2026)
- [Network Inversion for Uncertainty-Aware Out-of-Distribution Detection](https://mlsanity.com/paper/2505.23448/) (2025)
- [Fairness-Aware Multi-view Evidential Learning with Adaptive Prior](https://mlsanity.com/paper/2508.12997/) (2025)
- [Machine Learning for Infectious Disease Risk Prediction: A Survey](https://mlsanity.com/paper/2308.03037/) (2023)
- [Reliable Radiologic Skeletal Muscle Area Assessment -- A Biomarker for Cancer Cachexia Diagnosis](https://mlsanity.com/paper/2503.16556/) (2025)
- [Guided Uncertainty Learning Using a Post-Hoc Evidential Meta-Model](https://mlsanity.com/paper/2509.24492/) (2025)
- [Perceive, Act and Correct: Confidence Is Not Enough for Hyperspectral Classification](https://mlsanity.com/paper/2511.10068/) (2025)
- [TIE: A Training-Inversion-Exclusion Framework for Visually Interpretable and Uncertainty-Guided Out-of-Distribution Detection](https://mlsanity.com/paper/2512.00229/) (2025)
- [Robust Uncertainty Estimation under Distribution Shift via Difference Reconstruction](https://mlsanity.com/paper/2601.19341/) (2026)
- [From Misclassifications to Outliers: Joint Reliability Assessment in Classification](https://mlsanity.com/paper/2603.03903/) (2026)
- [UA-Net: Uncertainty-Aware Network for TRISO Image Semantic Segmentation](https://mlsanity.com/paper/2604.15542/) (2026)
- [Post-hoc Selective Classification for Reliable Synthetic Image Detection](https://mlsanity.com/paper/2605.08574/) (2026)
- [BESplit: Bias-Compensated Split Federated Learning with Evidential Aggregation](https://mlsanity.com/paper/2605.17508/) (2026)
- [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://mlsanity.com/paper/2607.28248/) (2026)
- [Robust Evidential Learning Through Latent Consistency](https://mlsanity.com/paper/2610.01384/) (2026)

## Abstract (arXiv)

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to impose the uncertainty quantification capability so that the learned model can achieve desired performance in accuracy and uncertainty prediction simultaneously. However, training the model from scratch is computationally expensive and may not be feasible in many situations. In this work, we consider a more practical post-hoc uncertainty learning setting, where a well-trained base model is given, and we focus on the uncertainty quantification task at the second stage of training. We propose a novel Bayesian meta-model to augment pre-trained models with better uncertainty quantification abilities, which is effective and computationally efficient. Our proposed method requires no additional training data and is flexible enough to quantify different uncertainties and easily adapt to different application settings, including out-of-domain data detection, misclassification detection, and trustworthy transfer learning. We demonstrate our proposed meta-model approach's flexibility and superior empirical performance on these applications over multiple representative image classification benchmarks.