# Learning minimal volume uncertainty ellipsoids

arXiv: https://arxiv.org/abs/2405.02441 · HTML: https://mlsanity.com/paper/2405.02441/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 14 of 14)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Semi-supervised Deep Reinforcement Learning in Support of IoT and Smart City Services](https://mlsanity.com/paper/1810.04118/) (2018)
- [CELLO-3D: Estimating the Covariance of ICP in the Real World](https://mlsanity.com/paper/1810.01470/) (2018)
- [Regularized M-estimators of scatter matrix](https://mlsanity.com/paper/1405.2528/) (2014)
- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributions](https://mlsanity.com/paper/1506.05215/) (2015)
- [A New Approach to 3D ICP Covariance Estimation](https://mlsanity.com/paper/1909.05722/) (2019)
- [Learning to Estimate Without Bias](https://mlsanity.com/paper/2110.12403/) (2021)
- [Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques](https://mlsanity.com/paper/2211.02165/) (2022)
- [Shrinking the eigenvalues of M-estimators of covariance matrix](https://mlsanity.com/paper/2006.10005/) (2020)

## Built on by (most cited first, 2 of 2)

- [Coverage Guarantees for Pseudo-Calibrated Conformal Prediction under Distribution Shift](https://mlsanity.com/paper/2602.14913/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)

## Abstract (arXiv)

We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of jointly Gaussian data, we prove that the optimal ellipsoid is centered around the conditional mean and shaped as the conditional covariance matrix. In more practical cases, we propose a differentiable optimization approach for approximately computing the optimal ellipsoids using a neural network with proper calibration. Compared to existing methods, our network requires less storage and less computations in inference time, leading to accurate yet smaller ellipsoids. We demonstrate these advantages on four real-world localization datasets.