Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks

TL;DR

This work introduces the $(\mathbf{s},\mathcal{G}, α)$-Generalized Multicalibration (GMC) framework to post-process predictive models for multi-group fairness in multi-dimensional outputs. It develops a generalized calibration objective, an algorithm with convergence guarantees, and finite-sample analyses, showing how to enforce fairness across many subgroups and dimensions. The authors demonstrate GMC's versatility through three applications: de-biased text generation, prediction-set conditional coverage in hierarchical classification, and fair false-negative-rate control in image segmentation, with empirical results indicating improved fairness without substantial accuracy loss. Overall, GMC provides a unified, theoretically grounded approach to multi-group fairness across complex, multidimensional prediction tasks relevant to real-world AI systems.

Abstract

This paper introduces a framework for post-processing machine learning models so that their predictions satisfy multi-group fairness guarantees. Based on the celebrated notion of multicalibration, we introduce $(\mathbf{s},\mathcal{G}, α)-$GMC (Generalized Multi-Dimensional Multicalibration) for multi-dimensional mappings $\mathbf{s}$, constraint set $\mathcal{G}$, and a pre-specified threshold level $α$. We propose associated algorithms to achieve this notion in general settings. This framework is then applied to diverse scenarios encompassing different fairness concerns, including false negative rate control in image segmentation, prediction set conditional uncertainty quantification in hierarchical classification, and de-biased text generation in language models. We conduct numerical studies on several datasets and tasks.

Figures (8)

• Figure 1: A demo of hierarchical text classification using a subset of labels from the Web of Science dataset. kowsari2017HDLTex.
• Figure 2: The bias on outputting different types of sensitive attributes measured on the corpus data. The results for the synthetic data are deferred to the appendix.
• Figure 3: The deviation of prediction-set conditional coverage from the target.
• Figure 4: The deviation of the false negative rate from the target in image segmentation.
• Figure 5: A demonstration of the input data

Theorems & Definitions (35)

• Definition 1: $(\bm s,\mathcal{G}, \alpha)$-GMC
• Definition 2: The derivative of a functional
• Definition 3: Convexity of a functional
• Definition 4: $K_{\mathcal{L}}$-smoothness of a functional
• Theorem 1
• Definition 5: Dimension of the function class
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5