# On Pairwise Quantile Regression - Statistical Guarantees and Applications

Source: [On Pairwise Quantile Regression - Statistical Guarantees and Applications](<https://www.sota2.com/research/paper/6a4c881f85dba69fef8b28de>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-25T05:00:05.609Z

Authors: Romain Th\\'er\\'ezien, Stephan Cl\\'emen\\c{c}on, Fantin Girard, Hamza El-Abdouni

Published: 2026-07-05T17:51:59.000Z

## Abstract

Quantile regression provides a powerful tool for summarizing the conditional distribution of a real-valued random variable (r.v.) of interest $Y$ as a function of covariates $Z$ in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise setting, where the variable to be explained is a similarity score between two independent observations (e.g., pixelated ID photos used as input to biometric systems), and the explanatory variables consist of the pair of covariates attached to these observations, such as age or hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove generalization bounds and identify mild conditions under which fast learning rates can be achieved. Confirming the probabilistic analysis, experiments based on simulation data also provide solid empirical evidence of the validity of the methodology promoted here for pairwise quantile regression. Finally, its usefulness from an application perspective is demonstrated by a detailed study aimed at analyzing errors in similarity scoring for facial recognition.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Facial Recognition on Facial recognition Genuine Pairs](<https://www.sota2.com/research/sota/facial-recognition-on-facial-recognition-genuine-pairs.md>): Facial Recognition; Facial recognition Genuine Pairs; D2-score: 37.4.

- [Facial Recognition on Facial recognition Impostor Pairs](<https://www.sota2.com/research/sota/facial-recognition-on-facial-recognition-impostor-pairs.md>): Facial Recognition; Facial recognition Impostor Pairs; D2-score: 22.3.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2607.04431>)

[PDF](<https://arxiv.org/pdf/2607.04431.pdf>)