Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification
This work is significant for researchers and practitioners in machine learning who require calibrated uncertainty quantification in regression tasks, offering an incremental improvement over existing methods.
This paper tackles the problem of accurately quantifying uncertainty in regression by specifying the full quantile function. The authors developed new quantile methods that overcome the limitations of the traditional pinball loss, resulting in more accurate conditional quantiles and improved calibration.
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.