  Among the many ways of quantifying uncertainty in a regression setting,
specifying the full quantile function is attractive, as quantiles are amenable
to interpretation and evaluation. A model that predicts the true conditional
quantiles for each input, at all quantile levels, presents a correct and
efficient representation of the underlying uncertainty. To achieve this, many
current quantile-based methods focus on optimizing the so-called pinball loss.
However, this loss restricts the scope of applicable regression models, limits
the 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 for
selecting a trade-off between calibration and sharpness, optimize for
calibration of centered intervals, and produce more accurate conditional
quantiles. We provide a thorough experimental evaluation of our methods, which
includes a high dimensional uncertainty quantification task in nuclear fusion.
