Quantile regression, based on check loss, is a widely used inferential paradigm in Econometrics and Statistics. The conditional quantiles provide a robust alternative to classical conditional means, and also allow uncertainty quantification of the predictions, while making very few distributional assumptions. We consider the analogue of check loss in the binary classification setting. We assume that the conditional quantiles are smooth functions that can be learnt by Deep Neural Networks (DNNs). Subsequently, we compute the Lipschitz constant of the proposed loss, and also show that its curvature is bounded, under some regularity conditions. Consequently, recent results on the error rates and DNN architecture complexity become directly applicable.
We quantify the uncertainty of the class probabilities in terms of prediction intervals, and develop individualized confidence scores that can be used to decide whether a prediction is reliable or not at scoring time. By aggregating the confidence scores at the dataset level, we provide two additional metrics, model confidence, and retention rate, to complement the widely used classifier summaries. We also the robustness of the proposed non-parametric binary quantile classification framework are also studied, and we demonstrate how to obtain several univariate summary statistics of the conditional distributions, in particular conditional means, using smoothed conditional quantiles, allowing the use of explanation techniques like Shapley to explain the mean predictions. Finally, we demonstrate an efficient training regime for this loss based on Stochastic Gradient Descent with Lipschitz Adaptive Learning Rates (LALR).
Univ Lyon（里昂大学）；EnsL（里昂高等师范学校）；UCBL（克洛德·贝尔纳里昂第一大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；LIP（里昂信息学实验室）；ENS de Lyon（里昂高等师范学校）；UMPA UMR 5669（里昂高等师范学校数学与应用数学联合实验室）
High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference
School of Statistics and Data Science, Shanghai University of Finance and Economics（上海金融学院统计与数据科学学院）；School of Statistics and Data Science, Southeast University（东南大学统计与数据科学学院）；School of Statistics and Data Science, Shanghai University of International Business and Economics（上海国际商务学院统计与数据科学学院）
Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration
Institute of Statistics and Big Data, Renmin University of China（统计与大数据研究院，中国人民大学）；Department of Decision Analytics and Operations, City University of Hong Kong（决策分析与运营部门，香港城市大学）；School of Information, Renmin University of China（信息学院，中国人民大学）
