# Conformal Robust Set Estimation

arXiv: https://arxiv.org/abs/2604.18441 · HTML: https://mlsanity.com/paper/2604.18441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 20 Apr 2026.

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

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Label Noise Robustness of Conformal Prediction](https://mlsanity.com/paper/2209.14295/) (2022)
- [Split Conformal Prediction under Data Contamination](https://mlsanity.com/paper/2407.07700/) (2024)
- [Robust Conformal Outlier Detection under Contaminated Reference Data](https://mlsanity.com/paper/2502.04807/) (2025)
- [GROS: A General Robust Aggregation Strategy](https://mlsanity.com/paper/2402.15442/) (2024)

## Abstract (arXiv)

We introduce a robust conformal prediction method based on the half-mass radius dP(x):=infr>0:P(B(x,r))>1/2. Its empirical version is exactly the distance from a point to its k-th nearest neighbour, with k=lfloor n/2rfloor+1. The resulting conformal sets retain finite-sample marginal validity and asymptotically target the robust population central set Qba:=x∈Rd:dP(x)≤βα. We prove consistency in symmetric-difference probability, derive non-asymptotic exponential bounds and obtain the rate O((log n/n)1/2) under a local mass condition. Under the same local regularity on the uncontaminated law, we also establish quantitative O(η) stability, uniformly over arbitrary contaminations of sufficiently small mass η, prove Hausdorff convergence of the empirical central sets, and provide computable ball-based representations using only pairwise distances.