# Calibrated Data-Dependent Constraints with Exact Satisfaction Guarantees

arXiv: https://arxiv.org/abs/2301.06195 · HTML: https://mlsanity.com/paper/2301.06195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 15 Jan 2023.

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

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [Two-Player Games for Efficient Non-Convex Constrained Optimization](https://mlsanity.com/paper/1804.06500/) (2018)
- [Training Well-Generalizing Classifiers for Fairness Metrics and Other Data-Dependent Constraints](https://mlsanity.com/paper/1807.00028/) (2018)
- [Scalable Learning of Non-Decomposable Objectives](https://mlsanity.com/paper/1608.04802/) (2016)
- [SenSeI: Sensitive Set Invariance for Enforcing Individual Fairness](https://mlsanity.com/paper/2006.14168/) (2020)
- [Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization](https://mlsanity.com/paper/1605.09349/) (2016)
- [Robust Regression via Mutivariate Regression Depth](https://mlsanity.com/paper/1702.04656/) (2017)

## Abstract (arXiv)

We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate data-dependent constraints so that they are calibrated: enforcing the reformulated constraints guarantees that their expected value counterparts are satisfied with a user-prescribed probability. The resulting optimization problem is amendable to standard stochastic optimization algorithms, and we demonstrate the efficacy of our method on a fairness-sensitive classification task where we wish to guarantee the classifier's fairness (at test time).