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.

本文中，我们介绍了一种同时二元分位数回归（SBQR）的技术，可以独立于损失函数构建分位表示，对于检测越界样本和校准模型等问题具有优越性。