# HappyMap: A Generalized Multi-calibration Method

arXiv: https://arxiv.org/abs/2303.04379 · HTML: https://mlsanity.com/paper/2303.04379/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 52 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 30 of 32)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Preserving Statistical Validity in Adaptive Data Analysis](https://mlsanity.com/paper/1411.2664/) (2014)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [Improving Generalization in Meta-learning via Task Augmentation](https://mlsanity.com/paper/2007.13040/) (2020)
- [The Power of Contrast for Feature Learning: A Theoretical Analysis](https://mlsanity.com/paper/2110.02473/) (2021)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [Meta-Learning with Fewer Tasks through Task Interpolation](https://mlsanity.com/paper/2106.02695/) (2021)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data](https://mlsanity.com/paper/2302.06232/) (2023)
- [Adversarial Training Helps Transfer Learning via Better Representations](https://mlsanity.com/paper/2106.10189/) (2021)
- [Representation via Representations: Domain Generalization via Adversarially Learned Invariant Representations](https://mlsanity.com/paper/2006.11478/) (2020)
- [Freeze then Train: Towards Provable Representation Learning under Spurious Correlations and Feature Noise](https://mlsanity.com/paper/2210.11075/) (2022)
- [High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Data](https://mlsanity.com/paper/1804.03018/) (2018)

## Built on by (most cited first, 18 of 18)

- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Loss Minimization Yields Multicalibration for Large Neural Networks](https://mlsanity.com/paper/2304.09424/) (2023)
- [Conformal Prediction Sets Can Cause Disparate Impact](https://mlsanity.com/paper/2410.01888/) (2024)
- [Semi-Supervised Risk Control via Prediction-Powered Inference](https://mlsanity.com/paper/2412.11174/) (2024)
- [The Relationship between No-Regret Learning and Online Conformal Prediction](https://mlsanity.com/paper/2502.10947/) (2025)
- [Bridging Multicalibration and Out-of-distribution Generalization Beyond Covariate Shift](https://mlsanity.com/paper/2406.00661/) (2024)
- [Conditional Conformal Risk Adaptation](https://mlsanity.com/paper/2504.07611/) (2025)
- [A Generic Framework for Conformal Fairness](https://mlsanity.com/paper/2505.16115/) (2025)
- [Discretization-free Multicalibration through Loss Minimization over Tree Ensembles](https://mlsanity.com/paper/2505.17435/) (2025)
- [Efficient Swap Multicalibration of Elicitable Properties](https://mlsanity.com/paper/2511.04907/) (2025)
- [Robust Decision Making with Partially Calibrated Forecasts](https://mlsanity.com/paper/2510.23471/) (2025)
- [Multi-Group Proportional Representation in Retrieval](https://mlsanity.com/paper/2407.08571/) (2024)
- [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)
- [FAIRM: Learning invariant representations for algorithmic fairness and domain generalization with minimax optimality](https://mlsanity.com/paper/2404.01608/) (2024)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)

## Abstract (arXiv)

Multi-calibration is a powerful and evolving concept originating in the field of algorithmic fairness. For a predictor f that estimates the outcome y given covariates x, and for a function class C, multi-calibration requires that the predictor f(x) and outcome y are indistinguishable under the class of auditors in C. Fairness is captured by incorporating demographic subgroups into the class of functions~C. Recent work has shown that, by enriching the class C to incorporate appropriate propensity re-weighting functions, multi-calibration also yields target-independent learning, wherein a model trained on a source domain performs well on unseen, future, target domains(approximately) captured by the re-weightings. Formally, multi-calibration with respect to C bounds big|mathbbE(x,y)~ D[c(f(x),x)·(f(x)-y)]big| for all c ∈ C. In this work, we view the term (f(x)-y) as just one specific mapping, and explore the power of an enriched class of mappings. We propose textitHappyMap, a generalization of multi-calibration, which yields a wide range of new applications, including a new fairness notion for uncertainty quantification (conformal prediction), a novel technique for conformal prediction under covariate shift, and a different approach to analyzing missing data, while also yielding a unified understanding of several existing seemingly disparate algorithmic fairness notions and target-independent learning approaches. We give a single textitHappyMap meta-algorithm that captures all these results, together with a sufficiency condition for its success.