发表机构
LTCI, Télécom Paris Institut Polytechnique de Paris; Idémia; Télécom Sud-Paris, Institut Polytechnique de Paris（LTCI，巴黎电信理工学院; Idémia; 巴黎理工学院，南巴黎电信）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对传统分位数回归无法处理成对相似性响应变量的问题，该文提出成对分位数回归方法，基于U过程集中度结果推导统计保证，在人脸识别相似性评分误差分析中验证了方法有效性。
AI 中文摘要
分位数回归是一种强大工具，可在关注的实值随机变量Y大概率呈现大分散性的场景下，将其条件分布表示为协变量Z的函数，突破了标准最小二乘回归仅能提供有效信息/预测的适用局限。本文旨在将该方法扩展到成对场景：当待解释变量采用两个独立观测（例如作为生物识别系统输入数据的像素化身份证照片）之间的相似性函数形式，且解释变量采用观测的一对协变量（例如年龄或头发颜色）形式时，本文将该统计学习问题的解视为成对版弹球损失的经验极小化器，并为其建立理论保证。利用U过程的精确集中度结果，本文证明了泛化界，并确定了可实现快速学习率的温和条件。为验证概率分析结果，基于模拟数据的实验也为所提出的成对分位数回归方法的有效性提供了可靠的实证证据。最后，通过一项旨在分析人脸识别相似性评分误差的详细研究，证明了该方法在应用层面的实用价值。
英文摘要
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.
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