  High concentration episodes for NO$_2$ are increasingly dealt with by
authorities through traffic restrictions which are activated when air quality
deteriorates beyond certain thresholds. Foreseeing the probability that
pollutant concentrations reach those thresholds becomes thus a necessity.
Probabilistic forecasting is a family of techniques that allow for the
prediction of the expected distribution function instead of a single value. In
the case of NO$_2$, it allows for the calculation of future chances of
exceeding thresholds and to detect pollution peaks. We thoroughly compared 10
state of the art probabilistic predictive models, using them to predict the
distribution of NO$_2$ concentrations in a urban location for a set of
forecasting horizons (up to 60 hours). Quantile gradient boosted trees shows
the best performance, yielding the best results for both the expected value and
the forecast full distribution. Furthermore, we show how this approach can be
used to detect pollution peaks.
