  Quantile Regression (QR) provides a way to approximate a single conditional
quantile. To have a more informative description of the conditional
distribution, QR can be merged with deep learning techniques to simultaneously
estimate multiple quantiles. However, the minimisation of the QR-loss function
does not guarantee non-crossing quantiles, which affects the validity of such
predictions and introduces a critical issue in certain scenarios. In this
article, we propose a generic deep learning algorithm for predicting an
arbitrary number of quantiles that ensures the quantile monotonicity constraint
up to the machine precision and maintains its modelling performance with
respect to alternative models. The presented method is evaluated over several
real-world datasets obtaining state-of-the-art results as well as showing that
it scales to large-size data sets.
