  Nearly 1/3 of the sources listed in the Third Fermi Large Area Telescope
(LAT) catalog (3FGL) remain unassociated. It is possible that predicted and
even unanticipated gamma-ray source classes are present in these data waiting
to be discovered. Taking advantage of the excellent spectral capabilities
achieved by the Fermi LAT, we use machine learning classifiers (Random Forest
and XGBoost) to pinpoint potentially novel source classes in the unassociated
3FGL sample outside the Galactic plane. Here we report a total of 34
high-confidence Galactic candidates at |b| > 5 degrees. The currently favored
standard astrophysical interpretations for these objects are pulsars or
low-luminosity globular clusters hosting millisecond pulsars (MSPs). Yet, these
objects could also be interpreted as dark matter annihilation taking place in
ultra-faint dwarf galaxies or dark matter subhalos. Unfortunately, Fermi LAT
spectra are not sufficient to break degeneracies between the different
scenarios. Careful visual inspection of archival optical images reveals no
obvious evidence for low-luminosity globular clusters or ultra-faint dwarf
galaxies inside the 95% error ellipses. If these are pulsars, this would bring
the total number of MSPs at |b| > 5 degrees to 106. We find this number to be
in excellent agreement with predictions from a new population synthesis of MSPs
that predicts 100-126 high-latitude 3FGL MSPs depending on the choice of
high-energy emission model. If, however, these are dark matter substructures,
we can place upper limits on the number of Galactic subhalos surviving today
and on dark matter annihilation cross sections. These limits are beginning to
approach the canonical thermal relic cross section for dark matter particle
masses below ~100 GeV in the bottom quark annihilation channel.
