# Density-Informed Pseudo-Counts for Calibrated Evidential Deep Learning

arXiv: https://arxiv.org/abs/2602.01477 · HTML: https://mlsanity.com/paper/2602.01477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 57 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (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)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [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)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Uncertainty-Aware Deep Classifiers using Generative Models](https://mlsanity.com/paper/2006.04183/) (2020)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Beyond Deep Ensembles: A Large-Scale Evaluation of Bayesian Deep Learning under Distribution Shift](https://mlsanity.com/paper/2306.12306/) (2023)
- [As Confidence Aligns: Exploring the Effect of AI Confidence on Human Self-confidence in Human-AI Decision Making](https://mlsanity.com/paper/2501.12868/) (2025)

## Abstract (arXiv)

Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations and behavior under distributional shift remain poorly understood. In this work, we provide a principled statistical interpretation by proving that EDL training corresponds to amortized variational inference in a hierarchical Bayesian model with a tempered pseudo-likelihood. This perspective reveals a major drawback: standard EDL conflates epistemic and aleatoric uncertainty, leading to systematic overconfidence on out-of-distribution (OOD) inputs. To address this, we introduce Density-Informed Pseudo-count EDL (DIP-EDL), a new parametrization that decouples class prediction from the magnitude of uncertainty by separately estimating the conditional label distribution and the marginal covariate density. This separation preserves evidence in high-density regions while shrinking predictions toward a uniform prior for OOD data. Theoretically, we prove that DIP-EDL achieves asymptotic concentration. Empirically, we show that our method enhances interpretability and improves robustness and uncertainty calibration under distributional shift.