  Wireless traffic prediction is a fundamental enabler to proactive network
optimisation in beyond 5G. Forecasting extreme demand spikes and troughs due to
traffic mobility is essential to avoiding outages and improving energy
efficiency. Current state-of-the-art deep learning forecasting methods
predominantly focus on overall forecast performance and do not offer
probabilistic uncertainty quantification (UQ). Whilst Gaussian Process (GP)
models have UQ capability, it is not able to predict extreme values very well.
Here, we design a feature embedding (FE) kernel for a GP model to forecast
traffic demand with extreme values. Using real 4G base station data, we compare
our FE-GP performance against both conventional naive GPs, ARIMA models, as
well as demonstrate the UQ output. For short-term extreme value prediction, we
demonstrated a 32\% reduction vs. S-ARIMA and 17\% reduction vs. Naive-GP. For
long-term average value prediction, we demonstrated a 21\% reduction vs.
S-ARIMA and 12\% reduction vs. Naive-GP. The FE kernel also enabled us to
create a flexible trade-off between overall forecast accuracy against
peak-trough accuracy. The advantage over neural network (e.g. CNN, LSTM) is
that the probabilistic forecast uncertainty can inform us of the risk of
predictions, as well as the full posterior distribution of the forecast.
