# Unified Approach for Weakly Supervised Multicalibration

arXiv: https://arxiv.org/abs/2605.09857 · HTML: https://mlsanity.com/paper/2605.09857/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 3 of 3)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Arbitrariness and Social Prediction: The Confounding Role of Variance in Fair Classification](https://mlsanity.com/paper/2301.11562/) (2023)

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

- [ProbabilityBench: Model Evaluation and Calibration with Exact Ground-Truth Uncertainty](https://mlsanity.com/paper/2610.17016/) (2026)
- [Noisy-Label Calibration with Multiple Unreliable Labels](https://mlsanity.com/paper/2610.19543/) (2026)

## Abstract (arXiv)

Multicalibration requires predicted scores to agree with label probabilities across rich families of subgroups and score-dependent tests, but existing methods require clean input-label pairs for evaluation and post-processing. This assumption fails in weakly supervised learning (WSL) regimes -- including positive-unlabeled, unlabeled-unlabeled, and positive-confidence learning -- where clean labels are costly or unavailable even though reliable uncertainty estimates may be crucial. We address this gap by developing estimators of multicalibration error and post-hoc correction methods for WSL settings in which clean input-label pairs are unavailable. We propose a unified framework for estimating and correcting multicalibration under weak supervision by combining contamination-matrix risk rewrites with witness-based calibration constraints, yielding corrected multicalibration moments with finite-sample guarantees. We further propose weak-label multicalibration boost (WLMC), a generic post-hoc recalibration algorithm under weak supervision. Finally, we conduct experiments across multiple weak-supervision settings to evaluate multicalibration behavior and offer empirical insight into uncertainty estimation under weak supervision.