# Well-calibrated Model Uncertainty with Temperature Scaling for Dropout Variational Inference

arXiv: https://arxiv.org/abs/1909.13550 · HTML: https://mlsanity.com/paper/1909.13550/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2019.

## Built on by (most cited first, 30 of 36)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [Spatially Varying Label Smoothing: Capturing Uncertainty from Expert Annotations](https://mlsanity.com/paper/2104.05788/) (2021)
- [Towards Improving Calibration in Object Detection Under Domain Shift](https://mlsanity.com/paper/2209.07601/) (2022)
- [BayesCap: Bayesian Identity Cap for Calibrated Uncertainty in Frozen Neural Networks](https://mlsanity.com/paper/2207.06873/) (2022)
- [Class-Distribution-Aware Calibration for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2109.05263/) (2021)
- [Recalibration of Aleatoric and Epistemic Regression Uncertainty in Medical Imaging](https://mlsanity.com/paper/2104.12376/) (2021)
- [A Survey on Safe Multi-Modal Learning System](https://mlsanity.com/paper/2402.05355/) (2024)
- [Cal-DETR: Calibrated Detection Transformer](https://mlsanity.com/paper/2311.03570/) (2023)
- [On Calibrated Model Uncertainty in Deep Learning](https://mlsanity.com/paper/2206.07795/) (2022)
- [Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimation](https://mlsanity.com/paper/2412.07169/) (2024)
- [Revisiting Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2502.05964/) (2025)
- [Overcoming the Limitations of Localization Uncertainty: Efficient & Exact Non-Linear Post-Processing and Calibration](https://mlsanity.com/paper/2306.08981/) (2023)
- [Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2504.18346/) (2025)
- [Posterior Temperature Optimization in Variational Inference for Inverse Problems](https://mlsanity.com/paper/2106.07533/) (2021)
- [Decoupling of neural network calibration measures](https://mlsanity.com/paper/2406.02411/) (2024)
- [Enhancing Uncertainty Estimation in Semantic Segmentation via Monte-Carlo Frequency Dropout](https://mlsanity.com/paper/2501.11258/) (2025)
- [Realistic Conversational Question Answering with Answer Selection based on Calibrated Confidence and Uncertainty Measurement](https://mlsanity.com/paper/2302.05137/) (2023)
- [Evaluating Bayesian deep learning for radio galaxy classification](https://mlsanity.com/paper/2405.18351/) (2024)
- [CLUE: Neural Networks Calibration via Learning Uncertainty-Error alignment](https://mlsanity.com/paper/2505.22803/) (2025)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Unsupervised Model Drift Estimation with Batch Normalization Statistics for Dataset Shift Detection and Model Selection](https://mlsanity.com/paper/2107.00191/) (2021)
- [TransMorph: Transformer for unsupervised medical image registration](https://mlsanity.com/paper/2111.10480/) (2021)
- [Towards Unbiased Calibration using Meta-Regularization](https://mlsanity.com/paper/2303.15057/) (2023)
- [An Uncertainty Aided Framework for Learning based Liver T1ρ Mapping and Analysis](https://mlsanity.com/paper/2307.02736/) (2023)
- [On Calibration of Modern Quantized Efficient Neural Networks](https://mlsanity.com/paper/2309.13866/) (2023)
- [Improving Uncertainty-Error Correspondence in Deep Bayesian Medical Image Segmentation](https://mlsanity.com/paper/2409.03470/) (2024)
- [A Deep Learning Approach to Estimate Canopy Height and Uncertainty by Integrating Seasonal Optical, SAR and Limited GEDI LiDAR Data over Northern Forests](https://mlsanity.com/paper/2410.18108/) (2024)
- [Extending confidence calibration to generalised measures of variation](https://mlsanity.com/paper/2602.12975/) (2026)
- [Rethinking Soft Label in Label Distribution Learning Perspective](https://mlsanity.com/paper/2301.13444/) (2023)

## Abstract (arXiv)

Model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. The uncertainty does not represent the model error well. In this paper, temperature scaling is extended to dropout variational inference to calibrate model uncertainty. Expected uncertainty calibration error (UCE) is presented as a metric to measure miscalibration of uncertainty. The effectiveness of this approach is evaluated on CIFAR-10/100 for recent CNN architectures. Experimental results show, that temperature scaling considerably reduces miscalibration by means of UCE and enables robust rejection of uncertain predictions. The proposed approach can easily be derived from frequentist temperature scaling and yields well-calibrated model uncertainty. It is simple to implement and does not affect the model accuracy.