# Tail-Aware Geometry Learning for Conformal Ellipsoids

arXiv: https://arxiv.org/abs/2609.27221 · HTML: https://mlsanity.com/paper/2609.27221/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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 prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression](https://mlsanity.com/paper/2501.10533/) (2025)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Flexible Conformal Highest Predictive Conditional Density Sets](https://mlsanity.com/paper/2406.18052/) (2024)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Conformal Inference for Time Series over Graphs](https://mlsanity.com/paper/2510.11049/) (2025)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Learning minimal volume uncertainty ellipsoids](https://mlsanity.com/paper/2405.02441/) (2024)
- [Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference](https://mlsanity.com/paper/2606.00320/) (2026)

## Abstract (arXiv)

This paper studies multivariate conformal prediction (CP), a distribution-free uncertainty quantification framework with finite-sample coverage guarantees. The efficiency of multivariate prediction sets hinges critically on the residual geometry encoded by the nonconformity score, while existing minimum-volume methods rely on quantile thresholds that ignore tail residual severity and implicitly bind geometry learning to coverage level. We propose a tail-aware geometry learning framework for conformal ellipsoids that decouples tail sensitivity in geometry learning from the final coverage guarantee. Using a two-split design, we learn the metric matrix via volume minimization under a CVaR constraint on an estimation split, then apply standard conformal calibration on a held-out calibration split. The resulting problem is convex and admits a bounded-reweighting interpretation that prioritizes high-residual samples. Moreover, we theoretically characterize the trade-off between ellipsoidal volume and tail severity. Experimental results demonstrate the effectiveness of the proposed method.