# Conformal Uncertainty Sets for Robust Optimization

arXiv: https://arxiv.org/abs/2105.14957 · HTML: https://mlsanity.com/paper/2105.14957/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 13 of 13)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Inductive Conformal Martingales for Change-Point Detection](https://mlsanity.com/paper/1706.03415/) (2017)
- [A Practical Guide to Robust Optimization](https://mlsanity.com/paper/1501.02634/) (2015)

## Built on by (most cited first, 30 of 49)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Semiparametric conformal prediction](https://mlsanity.com/paper/2411.02114/) (2024)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Conformal Prediction for Stochastic Decision-Making of PV Power in Electricity Markets](https://mlsanity.com/paper/2403.20149/) (2024)
- [Conformalized Interval Arithmetic with Symmetric Calibration](https://mlsanity.com/paper/2408.10939/) (2024)
- [Multivariate Conformal Selection](https://mlsanity.com/paper/2505.00917/) (2025)
- [Exact and Approximate Conformal Inference for Multi-Output Regression](https://mlsanity.com/paper/2210.17405/) (2022)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Conformal Prediction for Hierarchical Data](https://mlsanity.com/paper/2411.13479/) (2024)
- [Adaptive Coverage Policies in Conformal Prediction](https://mlsanity.com/paper/2510.04318/) (2025)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Powerful batch conformal prediction for classification](https://mlsanity.com/paper/2411.02239/) (2024)
- [JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows](https://mlsanity.com/paper/2505.23196/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal prediction](https://mlsanity.com/paper/2503.14106/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Learning minimal volume uncertainty ellipsoids](https://mlsanity.com/paper/2405.02441/) (2024)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)

## Abstract (arXiv)

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.