# Multicalibration as Boosting for Regression

arXiv: https://arxiv.org/abs/2301.13767 · HTML: https://mlsanity.com/paper/2301.13767/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 9 of 9)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Practical Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/1803.01088/) (2018)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Sample Complexity of Uniform Convergence for Multicalibration](https://mlsanity.com/paper/2005.01757/) (2020)
- [Scaffolding Sets](https://mlsanity.com/paper/2111.03135/) (2021)

## Built on by (most cited first, 30 of 33)

- [Multicalibration for Confidence Scoring in LLMs](https://mlsanity.com/paper/2404.04689/) (2024)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Oracle Efficient Online Multicalibration and Omniprediction](https://mlsanity.com/paper/2307.08999/) (2023)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Swap Agnostic Learning, or Characterizing Omniprediction via Multicalibration](https://mlsanity.com/paper/2302.06726/) (2023)
- [Loss Minimization Yields Multicalibration for Large Neural Networks](https://mlsanity.com/paper/2304.09424/) (2023)
- [Human Expertise in Algorithmic Prediction](https://mlsanity.com/paper/2402.00793/) (2024)
- [Estimating Model Performance Under Covariate Shift Without Labels](https://mlsanity.com/paper/2401.08348/) (2024)
- [Group-wise oracle-efficient algorithms for online multi-group learning](https://mlsanity.com/paper/2406.05287/) (2024)
- [Oracle Efficient Algorithms for Groupwise Regret](https://mlsanity.com/paper/2310.04652/) (2023)
- [Multi-group Learning for Hierarchical Groups](https://mlsanity.com/paper/2402.00258/) (2024)
- [How Global Calibration Strengthens Multiaccuracy](https://mlsanity.com/paper/2504.15206/) (2025)
- [Networked Information Aggregation via Machine Learning](https://mlsanity.com/paper/2507.09683/) (2025)
- [When does a predictor know its own loss?](https://mlsanity.com/paper/2502.20375/) (2025)
- [Discretization-free Multicalibration through Loss Minimization over Tree Ensembles](https://mlsanity.com/paper/2505.17435/) (2025)
- [The Scope of Multicalibration: Characterizing Multicalibration via Property Elicitation](https://mlsanity.com/paper/2302.08507/) (2023)
- [Is this model reliable for everyone? Testing for strong calibration](https://mlsanity.com/paper/2307.15247/) (2023)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [Three Types of Calibration with Properties and their Semantic and Formal Relationships](https://mlsanity.com/paper/2504.18395/) (2025)
- [Sample-Efficient Omniprediction for Proper Losses](https://mlsanity.com/paper/2510.12769/) (2025)
- [Improved Bounds for Swap Multicalibration and Swap Omniprediction](https://mlsanity.com/paper/2505.20885/) (2025)
- [Integrating Expert Judgment and Algorithmic Decision Making: An Indistinguishability Framework](https://mlsanity.com/paper/2410.08783/) (2024)
- [Robust Decision Making with Partially Calibrated Forecasts](https://mlsanity.com/paper/2510.23471/) (2025)
- [Model Ensembling for Constrained Optimization](https://mlsanity.com/paper/2405.16752/) (2024)
- [Multiaccuracy and Multicalibration via Proxy Groups](https://mlsanity.com/paper/2503.02870/) (2025)
- [On the Convergence of Multicalibration Gradient Boosting](https://mlsanity.com/paper/2602.06773/) (2026)
- [Multicalibration Boosting: Theory, Convergence, and Transferability](https://mlsanity.com/paper/2605.24364/) (2026)
- [Uniform convergence of the smooth calibration error and its relationship with functional gradient](https://mlsanity.com/paper/2505.19396/) (2025)
- [The Hidden Game Problem](https://mlsanity.com/paper/2510.03845/) (2025)
- [L2-Regularized Empirical Risk Minimization Guarantees Small Smooth Calibration Error](https://mlsanity.com/paper/2510.13450/) (2025)

## Abstract (arXiv)

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.