Conformal Classification with Equalized Coverage for Adaptively Selected Groups

TL;DR

A conformal inference method is introduced to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features to find a practical compromise between efficiency and algorithmic fairness.

Abstract

This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect potential model limitations or biases. This can be useful to find a practical compromise between efficiency -- by providing informative predictions -- and algorithmic fairness -- by ensuring equalized coverage for the most sensitive groups. We demonstrate the validity and effectiveness of this method on simulated and real data sets.

Figures (41)

• Figure 1: Schematic visualization of the automatic sensitive attribute selection carried out by our Adaptively Fair Conformal Prediction (AFCP) method. This method is designed to find the attribute corresponding to the group most negatively affected by algorithmic bias, on a case-by-case basis.
• Figure 2: Prediction sets constructed with different methods for patients in groups negatively affected by algorithm bias. Our method (AFCP) is designed to provide informative prediction sets that are well-calibrated conditional on the automatically identified critical sensitive attribute.
• Figure 3: Performance of conformal prediction sets constructed by different methods on synthetic medical diagnosis data, as a function of the total number of training and calibration data points. Our method (AFCP) leads to more informative prediction sets (smaller average size) with more effective mitigation of algorithmic bias (higher conditional coverage). The error bars indicate 2 standard errors.
• Figure 4: Selection frequency of different attributes using our AFCP method and its variation, AFCP1, in the experiments of Figure \ref{['fig:main_exp_mc_sim_ndata']}. As the sample size increases, AFCP becomes more consistent in selecting the most relevant attribute, Color.
• Figure 5: Performance of prediction sets constructed by different methods on the Nursery data, as a function of the sample size. AFCP leads to more informative predictions with higher coverage conditional on the sensitive attribute, Parents' occupation (shown explicitly for level one).

Theorems & Definitions (12)

• Theorem 1
• Theorem A1
• Lemma A1
• Theorem A2
• Theorem A3
• Theorem A4
• proof : Proof of Theorem \ref{['thm:AFCP']}
• proof : Proof of Theorem \ref{['thm:AFCP_multi']}
• proof : Proof of Theorem \ref{['thm:AFCP_lc']}.
• proof : Proof of Theorem \ref{['thm:AFCP_od']}