Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Counterfactually Fair Conformal Prediction

Ozgur Guldogan, Neeraj Sarna, Yuanyuan Li, Michael Berger

TL;DR

This work addresses the challenge of ensuring individual-level counterfactual fairness for prediction sets, not just point predictions. It introduces Counterfactually Fair Conformal Prediction (CF-CP), a training-free procedure that symmetrizes conformity scores across protected-attribute interventions and feeds them into split conformal prediction to yield counterfactually fair sets with guaranteed marginal coverage. The authors prove that, under an invertible structural causal model and exchangeability, CF-CP achieves set-level counterfactual fairness while preserving the CP coverage guarantee, and they demonstrate empirically that CF-CP reduces counterfactual set disparity with only a modest increase in average set size across regression and classification tasks on synthetic and real data (Law School, Bios). This approach provides a simple, practical uncertainty quantification method that enforces individual-level fairness without retraining or reliance on the protected-attribute distribution, with strong potential for fair decision-making under uncertainty.

Abstract

While counterfactual fairness of point predictors is well studied, its extension to prediction sets--central to fair decision-making under uncertainty--remains underexplored. On the other hand, conformal prediction (CP) provides efficient, distribution-free, finite-sample valid prediction sets, yet does not ensure counterfactual fairness. We close this gap by developing Counterfactually Fair Conformal Prediction (CF-CP) that produces counterfactually fair prediction sets. Through symmetrization of conformity scores across protected-attribute interventions, we prove that CF-CP results in counterfactually fair prediction sets while maintaining the marginal coverage property. Furthermore, we empirically demonstrate that on both synthetic and real datasets, across regression and classification tasks, CF-CP achieves the desired counterfactual fairness and meets the target coverage rate with minimal increase in prediction set size. CF-CP offers a simple, training-free route to counterfactually fair uncertainty quantification.

Counterfactually Fair Conformal Prediction

TL;DR

This work addresses the challenge of ensuring individual-level counterfactual fairness for prediction sets, not just point predictions. It introduces Counterfactually Fair Conformal Prediction (CF-CP), a training-free procedure that symmetrizes conformity scores across protected-attribute interventions and feeds them into split conformal prediction to yield counterfactually fair sets with guaranteed marginal coverage. The authors prove that, under an invertible structural causal model and exchangeability, CF-CP achieves set-level counterfactual fairness while preserving the CP coverage guarantee, and they demonstrate empirically that CF-CP reduces counterfactual set disparity with only a modest increase in average set size across regression and classification tasks on synthetic and real data (Law School, Bios). This approach provides a simple, practical uncertainty quantification method that enforces individual-level fairness without retraining or reliance on the protected-attribute distribution, with strong potential for fair decision-making under uncertainty.

Abstract

While counterfactual fairness of point predictors is well studied, its extension to prediction sets--central to fair decision-making under uncertainty--remains underexplored. On the other hand, conformal prediction (CP) provides efficient, distribution-free, finite-sample valid prediction sets, yet does not ensure counterfactual fairness. We close this gap by developing Counterfactually Fair Conformal Prediction (CF-CP) that produces counterfactually fair prediction sets. Through symmetrization of conformity scores across protected-attribute interventions, we prove that CF-CP results in counterfactually fair prediction sets while maintaining the marginal coverage property. Furthermore, we empirically demonstrate that on both synthetic and real datasets, across regression and classification tasks, CF-CP achieves the desired counterfactual fairness and meets the target coverage rate with minimal increase in prediction set size. CF-CP offers a simple, training-free route to counterfactually fair uncertainty quantification.

Paper Structure

This paper contains 41 sections, 6 theorems, 30 equations, 3 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Paper organization.
  4. Background: Conformal Prediction
  5. Notation and Setup.
  6. Split Conformal Prediction
  7. Counterfactual Fairness
  8. Point predictors
  9. Prediction sets
  10. Counterfactually Fair Conformal Prediction (CF-CP)
  11. Score Symmetrization and CF-CP Sets
  12. Aggregator choices.
  13. Computational overhead.
  14. Baselines and Comparisons
  15. Retraining-based approaches.
  16. ...and 26 more sections

Key Result

Lemma 4.1

Let Assumption assump:invertible hold. Fix any $y\in\mathcal{Y}$. Then for all $a,a'\in\mathcal{A}$,

Figures (3)

  • Figure 1: Counterfactual Set Disparity (CSD) vs noise level in counterfactual generation. It shows that CF-CP methods show similar robustness to noise as other counterfactual fair models.
  • Figure 2: Causal Graphs of the Datasets Used in Experiments
  • Figure 3: Counterfactual Set Disparity (CSD) vs noise level in counterfactual generation for APS(left) and RAPS (right) base scores on synthetic classification dataset (mean over 10 runs).

Theorems & Definitions (10)

  • Definition 3.1: Counterfactual Fairness---point predictor
  • Definition 3.2: Counterfactual fairness---prediction sets
  • Lemma 4.1: Invariance of the symmetrized score
  • Corollary 4.1: Set-level counterfactual invariance
  • Theorem 4.1: Exchangeability preservation
  • Corollary 4.2: Marginal coverage for CF-CP
  • Lemma A.1: Invariance of the symmetrized score
  • proof
  • Theorem A.1: Exchangeability preservation
  • proof