Distribution-informed Efficient Conformal Prediction for Full Ranking

TL;DR

This paper introduces Distribution-informed Conformal Ranking (DCR), a method that leverages the exact distribution of non-conformity scores to produce more efficient and valid prediction sets for full ranking uncertainty quantification.

Contribution

DCR derives the distribution of non-conformity scores using Negative Hypergeometric distributions, improving prediction set efficiency over existing methods.

Findings

Reduces average prediction set size by up to 36%.

Maintains valid coverage with improved efficiency.

Theoretically guarantees coverage under mild assumptions.

Abstract

Quantifying uncertainty is critical for the safe deployment of ranking models in real-world applications. Recent work offers a rigorous solution using conformal prediction in a full ranking scenario, which aims to construct prediction sets for the absolute ranks of test items based on the relative ranks of calibration items. However, relying on upper bounds of non-conformity scores renders the method overly conservative, resulting in substantially large prediction sets. To address this, we propose Distribution-informed Conformal Ranking (DCR), which produces efficient prediction sets by deriving the exact distribution of non-conformity scores. In particular, we find that the absolute ranks of calibration items follow Negative Hypergeometric distributions, conditional on their relative ranks. DCR thus uses the rank distribution to derive non-conformity score distribution and determine conformal thresholds. We provide theoretical guarantees that DCR achieves improved efficiency over the baseline while ensuring valid coverage under mild assumptions. Extensive experiments demonstrate the superiority of DCR, reducing average prediction set size by up to 36%, while maintaining valid coverage.