# How Global Calibration Strengthens Multiaccuracy

arXiv: https://arxiv.org/abs/2504.15206 · HTML: https://mlsanity.com/paper/2504.15206/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Multicalibration as Boosting for Regression](https://mlsanity.com/paper/2301.13767/) (2023)
- [Near-Optimal Algorithms for Omniprediction](https://mlsanity.com/paper/2501.17205/) (2025)
- [Swap Agnostic Learning, or Characterizing Omniprediction via Multicalibration](https://mlsanity.com/paper/2302.06726/) (2023)
- [When is Multicalibration Post-Processing Necessary?](https://mlsanity.com/paper/2406.06487/) (2024)
- [Complexity-Theoretic Implications of Multicalibration](https://mlsanity.com/paper/2312.17223/) (2023)
- [From Pseudorandomness to Multi-Group Fairness and Back](https://mlsanity.com/paper/2301.08837/) (2023)
- [Multicalibrated Partitions for Importance Weights](https://mlsanity.com/paper/2103.05853/) (2021)
- [Characterizing the Distinguishability of Product Distributions through Multicalibration](https://mlsanity.com/paper/2412.03562/) (2024)
- [Generative Models of Huge Objects](https://mlsanity.com/paper/2302.12823/) (2023)
- [The Sample Complexity of Smooth Boosting and the Tightness of the Hardcore Theorem](https://mlsanity.com/paper/2409.11597/) (2024)

## Built on by (most cited first, 8 of 8)

- [Networked Information Aggregation via Machine Learning](https://mlsanity.com/paper/2507.09683/) (2025)
- [Generalized and Unified Equivalences between Hardness and Pseudoentropy](https://mlsanity.com/paper/2507.05972/) (2025)
- [Efficient Swap Multicalibration of Elicitable Properties](https://mlsanity.com/paper/2511.04907/) (2025)
- [Supersimulators](https://mlsanity.com/paper/2509.17994/) (2025)
- [An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to Phi-Regret Minimization](https://mlsanity.com/paper/2604.19592/) (2026)
- [Robust Learning with Optimal Error](https://mlsanity.com/paper/2604.02555/) (2026)
- [Auditability and the Landscape of Distance to Multicalibration](https://mlsanity.com/paper/2509.16930/) (2025)
- [Defensive Boosting for Online Probabilistic Forecasting](https://mlsanity.com/paper/2608.13554/) (2026)

## Abstract (arXiv)

Multiaccuracy and multicalibration are multigroup fairness notions for prediction that have found numerous applications in learning and computational complexity. They can be achieved from a single learning primitive: weak agnostic learning. Here we investigate the power of multiaccuracy as a learning primitive, both with and without the additional assumption of calibration. We find that multiaccuracy in itself is rather weak, but that the addition of global calibration (this notion is called calibrated multiaccuracy) boosts its power substantially, enough to recover implications that were previously known only assuming the stronger notion of multicalibration. We give evidence that multiaccuracy might not be as powerful as standard weak agnostic learning, by showing that there is no way to post-process a multiaccurate predictor to get a weak learner, even assuming the best hypothesis has correlation 1/2. Rather, we show that it yields a restricted form of weak agnostic learning, which requires some concept in the class to have correlation greater than 1/2 with the labels. However, by also requiring the predictor to be calibrated, we recover not just weak, but strong agnostic learning. A similar picture emerges when we consider the derivation of hardcore measures from predictors satisfying multigroup fairness notions. On the one hand, while multiaccuracy only yields hardcore measures of density half the optimal, we show that (a weighted version of) calibrated multiaccuracy achieves optimal density. Our results yield new insights into the complementary roles played by multiaccuracy and calibration in each setting. They shed light on why multiaccuracy and global calibration, although not particularly powerful by themselves, together yield considerably stronger notions.