# Distance-Based Learning from Errors for Confidence Calibration

arXiv: https://arxiv.org/abs/1912.01730 · HTML: https://mlsanity.com/paper/1912.01730/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

## Built on by (most cited first, 23 of 23)

- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [DOCTOR: A Simple Method for Detecting Misclassification Errors](https://mlsanity.com/paper/2106.02395/) (2021)
- [Energy-Based Open-World Uncertainty Modeling for Confidence Calibration](https://mlsanity.com/paper/2107.12628/) (2021)
- [Rethinking Confidence Calibration for Failure Prediction](https://mlsanity.com/paper/2303.02970/) (2023)
- [Corner Cases for Visual Perception in Automated Driving: Some Guidance on Detection Approaches](https://mlsanity.com/paper/2102.05897/) (2021)
- [Synergizing between Self-Training and Adversarial Learning for Domain Adaptive Object Detection](https://mlsanity.com/paper/2110.00249/) (2021)
- [Noise-resistant Deep Metric Learning with Ranking-based Instance Selection](https://mlsanity.com/paper/2103.16047/) (2021)
- [Revisiting Confidence Estimation: Towards Reliable Failure Prediction](https://mlsanity.com/paper/2403.02886/) (2024)
- [How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2308.12252/) (2023)
- [ProtoInfoMax: Prototypical Networks with Mutual Information Maximization for Out-of-Domain Detection](https://mlsanity.com/paper/2108.12229/) (2021)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [DIRA: Dynamic Domain Incremental Regularised Adaptation](https://mlsanity.com/paper/2205.00147/) (2022)
- [PercentMatch: Percentile-based Dynamic Thresholding for Multi-Label Semi-Supervised Classification](https://mlsanity.com/paper/2208.13946/) (2022)
- [Perception and Semantic Aware Regularization for Sequential Confidence Calibration](https://mlsanity.com/paper/2305.19498/) (2023)
- [A Method of Moments Embedding Constraint and its Application to Semi-Supervised Learning](https://mlsanity.com/paper/2404.17978/) (2024)
- [Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy](https://mlsanity.com/paper/2412.14223/) (2024)
- [How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2508.09346/) (2025)
- [Noise-Resistant Deep Metric Learning with Probabilistic Instance Filtering](https://mlsanity.com/paper/2108.01431/) (2021)
- [A Geometric Method for Improved Uncertainty Estimation in Real-time](https://mlsanity.com/paper/2206.11562/) (2022)
- [Uncertainty Estimation based on Geometric Separation](https://mlsanity.com/paper/2301.04452/) (2023)
- [Uncertainty-aware Sampling for Long-tailed Semi-supervised Learning](https://mlsanity.com/paper/2401.04435/) (2024)

## Abstract (arXiv)

Deep neural networks (DNNs) are poorly calibrated when trained in conventional ways. To improve confidence calibration of DNNs, we propose a novel training method, distance-based learning from errors (DBLE). DBLE bases its confidence estimation on distances in the representation space. In DBLE, we first adapt prototypical learning to train classification models. It yields a representation space where the distance between a test sample and its ground truth class center can calibrate the model's classification performance. At inference, however, these distances are not available due to the lack of ground truth labels. To circumvent this by inferring the distance for every test sample, we propose to train a confidence model jointly with the classification model. We integrate this into training by merely learning from mis-classified training samples, which we show to be highly beneficial for effective learning. On multiple datasets and DNN architectures, we demonstrate that DBLE outperforms alternative single-model confidence calibration approaches. DBLE also achieves comparable performance with computationally-expensive ensemble approaches with lower computational cost and lower number of parameters.