The simultaneous quantile regression (SQR) technique has been used to estimate uncertainties for deep learning models, but its application is limited by the requirement that the solution at the median quantile ({\tau} = 0.5) must minimize the mean absolute error (MAE). In this article, we address this limitation by demonstrating a duality between quantiles and estimated probabilities in the case of simultaneous binary quantile regression (SBQR). This allows us to decouple the construction of quantile representations from the loss function, enabling us to assign an arbitrary classifier f(x) at the median quantile and generate the full spectrum of SBQR quantile representations at different {\tau} values. We validate our approach through two applications: (i) detecting out-of-distribution samples, where we show that quantile representations outperform standard probability outputs, and (ii) calibrating models, where we demonstrate the robustness of quantile representations to distortions. We conclude with a discussion of several hypotheses arising from these findings.

翻译：同步分位数回归（SQR）技术已被用于估计深度学习模型的不确定性，但其应用受到中位数分位数（τ=0.5）处解必须最小化平均绝对误差（MAE）这一要求的限制。在本文中，我们通过证明同步二元分位数回归（SBQR）中分位数与估计概率之间的对偶性来解决这一限制。这使我们能够将分位数表示的构建与损失函数解耦，从而在中位数分位数处分配任意分类器f(x)，并生成不同τ值下SBQR分位数表示的完整谱系。我们通过两个应用验证了我们的方法：（i）检测分布外样本，其中我们证明分位数表示优于标准概率输出；（ii）校准模型，其中我们展示了分位数表示对失真的鲁棒性。最后，我们讨论了由这些发现引发的若干假设。