Decoupling Quantile Representations from Loss Function

Aditya Challa, Soma S Dhavala, Snehanshu Saha

Keywords: Quantiles, Duality, Calibration, OOD Detection, simultaneous binary quantile regression (SBQR), invariant to distortion

Abstract:

The simultaneous quantile regression (SQR) technique has been used to estimate 2 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.

Submission Number: 4125