HappyMap : A Generalized Multicalibration Method

Authors Zhun Deng, Cynthia Dwork, Linjun Zhang



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Zhun Deng
  • Department of Computer Science, Columbia University, New York, NY, USA
Cynthia Dwork
  • Department of Computer Science, Harvard University, Cambridge, MA, USA
Linjun Zhang
  • Department of Statistics, Rutgers University, Piscataway, NJ, USA

Acknowledgements

We thank all the reviewers for their comments and suggestions. We are indebted to Aaron Roth for his insightful and valuable feedback, which greatly improved the paper.

Cite AsGet BibTex

Zhun Deng, Cynthia Dwork, and Linjun Zhang. HappyMap : A Generalized Multicalibration Method. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 41:1-41:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITCS.2023.41

Abstract

Multicalibration 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, multicalibration with respect to C bounds |𝔼_{(x,y)∼D}[c(f(x),x)⋅(f(x)-y)]| 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 s-Happy Multicalibration, a generalization of multi-calibration, which yields a wide range of new applications, including a new fairness notion for uncertainty quantification, 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 HappyMap meta-algorithm that captures all these results, together with a sufficiency condition for its success.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Theory and algorithms for application domains
Keywords
  • algorithmic fairness
  • target-independent learning
  • transfer learning

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