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Among the many ways of quantifying uncertainty in a regression setting,specifying the full quantile function is attractive, as quantiles are amenableto interpretation and evaluation. A model that predicts the true conditionalquantiles for each input, at all quantile levels, presents a correct andefficient representation of the underlying uncertainty. To achieve this, manycurrent quantile-based methods focus on optimizing the so-called pinball loss.However, this loss restricts the scope of applicable regression models, limitsthe ability to target many desirable properties (e.g. calibration, sharpness,centered intervals), and may produce poor conditional quantiles. In this work,we develop new quantile methods that address these shortcomings. In particular,we propose methods that can apply to any class of regression model, allow forselecting a trade-off between calibration and sharpness, optimize forcalibration of centered intervals, and produce more accurate conditionalquantiles. We provide a thorough experimental evaluation of our methods, whichincludes a high dimensional uncertainty quantification task in nuclear fusion.

Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification