# An Uncertainty-aware Loss Function for Training Neural Networks with Calibrated Predictions

arXiv: https://arxiv.org/abs/2110.03260 · HTML: https://mlsanity.com/paper/2110.03260/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [SleepTransformer: Automatic Sleep Staging with Interpretability and Uncertainty Quantification](https://mlsanity.com/paper/2105.11043/) (2021)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [Deep Directional Statistics: Pose Estimation with Uncertainty Quantification](https://mlsanity.com/paper/1805.03430/) (2018)
- [Bayesian Image Quality Transfer with CNNs: Exploring Uncertainty in dMRI Super-Resolution](https://mlsanity.com/paper/1705.00664/) (2017)
- [A Vision-based System for Traffic Anomaly Detection using Deep Learning and Decision Trees](https://mlsanity.com/paper/2104.06856/) (2021)
- [An Uncertainty-aware Transfer Learning-based Framework for Covid-19 Diagnosis](https://mlsanity.com/paper/2007.14846/) (2020)
- [Objective Evaluation of Deep Uncertainty Predictions for COVID-19 Detection](https://mlsanity.com/paper/2012.11840/) (2020)
- [I Find Your Lack of Uncertainty in Computer Vision Disturbing](https://mlsanity.com/paper/2104.08188/) (2021)
- [Uncertainty Quantification for Sparse Deep Learning](https://mlsanity.com/paper/2002.11815/) (2020)
- [Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements](https://mlsanity.com/paper/2103.01259/) (2021)
- [Prediction Surface Uncertainty Quantification in Object Detection Models for Autonomous Driving](https://mlsanity.com/paper/2107.04991/) (2021)
- [Uncertainty-Aware Credit Card Fraud Detection Using Deep Learning](https://mlsanity.com/paper/2107.13508/) (2021)
- [UncertaintyFuseNet: Robust Uncertainty-aware Hierarchical Feature Fusion Model with Ensemble Monte Carlo Dropout for COVID-19 Detection](https://mlsanity.com/paper/2105.08590/) (2021)
- [Uncertainty Quantification for Deep Context-Aware Mobile Activity Recognition and Unknown Context Discovery](https://mlsanity.com/paper/2003.01753/) (2020)
- [Detecting Adversarial Examples for Speech Recognition via Uncertainty Quantification](https://mlsanity.com/paper/2005.14611/) (2020)
- [Uncertainty-Aware Organ Classification for Surgical Data Science Applications in Laparoscopy](https://mlsanity.com/paper/1706.07002/) (2017)
- [Confidence Aware Neural Networks for Skin Cancer Detection](https://mlsanity.com/paper/2107.09118/) (2021)
- [Informed MCMC with Bayesian Neural Networks for Facial Image Analysis](https://mlsanity.com/paper/1811.07969/) (2018)

## Built on by (most cited first, 6 of 6)

- [Error-Driven Uncertainty Aware Training](https://mlsanity.com/paper/2405.01205/) (2024)
- [Uncertainty Estimation by Human Perception versus Neural Models](https://mlsanity.com/paper/2506.15850/) (2025)
- [CLUE: Neural Networks Calibration via Learning Uncertainty-Error alignment](https://mlsanity.com/paper/2505.22803/) (2025)
- [Enhanced Uncertainty Estimation in Ultrasound Image Segmentation with MSU-Net](https://mlsanity.com/paper/2407.21273/) (2024)
- [The Craft of Selective Prediction: Towards Reliable Case Outcome Classification -- An Empirical Study on European Court of Human Rights Cases](https://mlsanity.com/paper/2409.18645/) (2024)
- [Beyond Uncertainty Quantification: Learning Uncertainty for Trust-Informed Neural Network Decisions - A Case Study in COVID-19 Classification](https://mlsanity.com/paper/2410.02805/) (2024)

## Abstract (arXiv)

Uncertainty quantification of machine learning and deep learning methods plays an important role in enhancing trust to the obtained result. In recent years, a numerous number of uncertainty quantification methods have been introduced. Monte Carlo dropout (MC-Dropout) is one of the most well-known techniques to quantify uncertainty in deep learning methods. In this study, we propose two new loss functions by combining cross entropy with Expected Calibration Error (ECE) and Predictive Entropy (PE). The obtained results clearly show that the new proposed loss functions lead to having a calibrated MC-Dropout method. Our results confirmed the great impact of the new hybrid loss functions for minimising the overlap between the distributions of uncertainty estimates for correct and incorrect predictions without sacrificing the model's overall performance.