  The paucity of hypervelocity stars (HVSs) known to date has severely hampered
their potential to investigate the stellar population of the Galactic Centre
and the Galactic Potential. The first Gaia data release gives an opportunity to
increase the current sample. The challenge is the disparity between the
expected number of hypervelocity stars and that of bound background stars. We
have applied a novel data mining algorithm based on machine learning
techniques, an artificial neural network, to the Tycho-Gaia astrometric
solution (TGAS) catalogue. With no pre-selection of data, we could exclude
immediately $\sim 99 \%$ of the stars in the catalogue and find 80 candidates
with more than $90\%$ predicted probability to be HVSs, based only on their
position, proper motions, and parallax. We have cross-checked our findings with
other spectroscopic surveys, determining radial velocities for 30 and
spectroscopic distances for 5 candidates. In addition, follow-up observations
have been carried out at the Isaac Newton Telescope for 22 stars, for which we
obtained radial velocities and distance estimates. We discover 14 stars with a
total velocity in the Galactic rest frame > 400 km/s, and 5 of these have a
probability $>50\%$ of being unbound from the Milky Way. Tracing back their
orbits in different Galactic potential models we find one possible unbound HVS
with velocity $\sim$ 520 km/s, 5 bound HVSs, and, notably, 5 runaway stars with
median velocity between 400 and 780 km/s. At the moment, uncertainties in the
distance estimates and ages are too large to confirm the nature of our
candidates by narrowing down their ejection location, and we wait for future
Gaia releases to validate the quality of our sample. This test successfully
demonstrates the feasibility of our new data mining routine.
