# Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts

arXiv: https://arxiv.org/abs/2006.09239 · HTML: https://mlsanity.com/paper/2006.09239/

## Key facts

- Cited by 164 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 30 of 164)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Trusted Multi-View Classification with Dynamic Evidential Fusion](https://mlsanity.com/paper/2204.11423/) (2022)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Evidential Deep Learning for Open Set Action Recognition](https://mlsanity.com/paper/2107.10161/) (2021)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [Provable Dynamic Fusion for Low-Quality Multimodal Data](https://mlsanity.com/paper/2306.02050/) (2023)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Uncertainty in Natural Language Processing: Sources, Quantification, and Applications](https://mlsanity.com/paper/2306.04459/) (2023)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Uncertainty-Aware Machine Translation Evaluation](https://mlsanity.com/paper/2109.06352/) (2021)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [Post-hoc Uncertainty Learning using a Dirichlet Meta-Model](https://mlsanity.com/paper/2212.07359/) (2022)
- [Behavioral Intention Prediction in Driving Scenes: A Survey](https://mlsanity.com/paper/2211.00385/) (2022)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [Bridging the Vision-Brain Gap with an Uncertainty-Aware Blur Prior](https://mlsanity.com/paper/2503.04207/) (2025)
- [OODformer: Out-Of-Distribution Detection Transformer](https://mlsanity.com/paper/2107.08976/) (2021)
- [Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2206.01558/) (2022)
- [Towards Open Set Video Anomaly Detection](https://mlsanity.com/paper/2208.11113/) (2022)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Interpretable Self-Aware Neural Networks for Robust Trajectory Prediction](https://mlsanity.com/paper/2211.08701/) (2022)
- [Shedding Light on Large Generative Networks: Estimating Epistemic Uncertainty in Diffusion Models](https://mlsanity.com/paper/2406.18580/) (2024)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)

## Abstract (arXiv)

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.