  Very recently, the IceCube Collaboration reported a flux of neutrinos in the
energy range 50 TeV < E_\nu < 2 PeV, which departs from expectations from
atmospheric background at the 5.7\sigma level. This flux is in remarkable
agreement with the expected diffuse flux of neutrinos from starburst galaxies,
and the 3 highest energy events have uncertainty contours encompassing some of
such systems. These events, all of which have well-measured energies above 1
PeV, exhibit shower topologies, for which the angular resolution is about
15^\circ. Due to this angular uncertainty and the a posteriori nature of cuts
used in our study it is not possible to assign a robust statistical
significance to this association. Using muon tracks, which have angular
resolution < 1^\circ, we compute the number of observations required to make a
statistically significant statement, and show that in a few years of operation
the upgraded IceCube detector should be able to confirm or refute this
hypothesis. We also note that double bang topology rates constitute a possible
discriminator among various astrophysical sources.
