# The Bayesian Confidence (BACON) Estimator for Deep Neural Networks

arXiv: https://arxiv.org/abs/2410.12604 · HTML: https://mlsanity.com/paper/2410.12604/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [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)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Confidence Calibration for Domain Generalization under Covariate Shift](https://mlsanity.com/paper/2104.00742/) (2021)
- [Estimating Expected Calibration Errors](https://mlsanity.com/paper/2109.03480/) (2021)

## Abstract (arXiv)

This paper introduces the Bayesian Confidence Estimator (BACON) for deep neural networks. Current practice of interpreting Softmax values in the output layer as probabilities of outcomes is prone to extreme predictions of class probability. In this work we extend Waagen's method of representing the terminal layers with a geometric model, where the probability associated with an output vector is estimated with Bayes' Rule using validation data to provide likelihood and normalization values. This estimator provides superior ECE and ACE calibration error compared to Softmax for ResNet-18 at 85% network accuracy, and EfficientNet-B0 at 95% network accuracy, on the CIFAR-10 dataset with an imbalanced test set, except for very high accuracy edge cases. In addition, when using the ACE metric, BACON demonstrated improved calibration error when estimating probabilities for the imbalanced test set when using actual class distribution fractions.