# Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection

arXiv: https://arxiv.org/abs/2207.01242 · HTML: https://mlsanity.com/paper/2207.01242/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 4 Jul 2022.

## Builds on (most cited first, 21 of 21)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Bounding Box Regression with Uncertainty for Accurate Object Detection](https://mlsanity.com/paper/1809.08545/) (2018)
- [A Review and Comparative Study on Probabilistic Object Detection in Autonomous Driving](https://mlsanity.com/paper/2011.10671/) (2020)
- [Multivariate Confidence Calibration for Object Detection](https://mlsanity.com/paper/2004.13546/) (2020)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [BayesOD: A Bayesian Approach for Uncertainty Estimation in Deep Object Detectors](https://mlsanity.com/paper/1903.03838/) (2019)
- [Probabilistic Object Detection: Definition and Evaluation](https://mlsanity.com/paper/1811.10800/) (2018)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [Can We Trust You? On Calibration of a Probabilistic Object Detector for Autonomous Driving](https://mlsanity.com/paper/1909.12358/) (2019)
- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [From Black-box to White-box: Examining Confidence Calibration under different Conditions](https://mlsanity.com/paper/2101.02971/) (2021)
- [f-Cal: Calibrated aleatoric uncertainty estimation from neural networks for robot perception](https://mlsanity.com/paper/2109.13913/) (2021)

## Built on by (most cited first, 9 of 9)

- [Towards Building Self-Aware Object Detectors via Reliable Uncertainty Quantification and Calibration](https://mlsanity.com/paper/2307.00934/) (2023)
- [MoCaE: Mixture of Calibrated Experts Significantly Improves Object Detection](https://mlsanity.com/paper/2309.14976/) (2023)
- [Multi-fidelity Gaussian process surrogate modeling for regression problems in physics](https://mlsanity.com/paper/2404.11965/) (2024)
- [A Theoretical and Practical Framework for Evaluating Uncertainty Calibration in Object Detection](https://mlsanity.com/paper/2309.00464/) (2023)
- [Evaluating the Quality of the Quantified Uncertainty for (Re)Calibration of Data-Driven Regression Models](https://mlsanity.com/paper/2508.17761/) (2025)
- [A systematic evaluation of uncertainty quantification techniques in deep learning: a case study in photoplethysmography signal analysis](https://mlsanity.com/paper/2511.00301/) (2025)
- [Bayesian Inference of Primordial Magnetic Field Parameters from CMB with Spherical Graph Neural Networks](https://mlsanity.com/paper/2510.20795/) (2025)
- [Rethinking Detection Calibration: A Coordinate and Direction Perspective](https://mlsanity.com/paper/2607.29040/) (2026)
- [Observation Quality in DSM-Assisted Aerial Localization: A Benchmark and Base-Anchored Uncertainty Calibration](https://mlsanity.com/paper/2610.18564/) (2026)

## Abstract (arXiv)

Reliable spatial uncertainty evaluation of object detection models is of special interest and has been subject of recent work. In this work, we review the existing definitions for uncertainty calibration of probabilistic regression tasks. We inspect the calibration properties of common detection networks and extend state-of-the-art recalibration methods. Our methods use a Gaussian process (GP) recalibration scheme that yields parametric distributions as output (e.g. Gaussian or Cauchy). The usage of GP recalibration allows for a local (conditional) uncertainty calibration by capturing dependencies between neighboring samples. The use of parametric distributions such as as Gaussian allows for a simplified adaption of calibration in subsequent processes, e.g., for Kalman filtering in the scope of object tracking. In addition, we use the GP recalibration scheme to perform covariance estimation which allows for post-hoc introduction of local correlations between the output quantities, e.g., position, width, or height in object detection. To measure the joint calibration of multivariate and possibly correlated data, we introduce the quantile calibration error which is based on the Mahalanobis distance between the predicted distribution and the ground truth to determine whether the ground truth is within a predicted quantile. Our experiments show that common detection models overestimate the spatial uncertainty in comparison to the observed error. We show that the simple Isotonic Regression recalibration method is sufficient to achieve a good uncertainty quantification in terms of calibrated quantiles. In contrast, if normal distributions are required for subsequent processes, our GP-Normal recalibration method yields the best results. Finally, we show that our covariance estimation method is able to achieve best calibration results for joint multivariate calibration.