  Starburst galaxies and star-forming regions in the Milkyway, with high rate
of supernova activities, are candidate sources of high-energy neutrinos. Using
a gamma-ray selected sample of these sources we perform statistical analysis of
their angular correlation with the four-year sample of high-energy starting
events (HESE), detected by the IceCube Neutrino Observatory. We find that the
two samples (starburst galaxies and local star-forming regions) are correlated
with cosmic neutrinos at $\sim (2-3)\sigma$ (pre-trial) significance level,
when the full HESE sample with deposited energy $\gtrsim 20$~TeV is considered.
However when we consider the HESE sample with deposited energy $\gtrsim
60$~TeV, which is almost free of atmospheric neutrino and muon backgrounds, the
significance of correlation decreased drastically. We perform a similar study
for Galactic sources in the 2nd Catalog of Hard {\em Fermi}-LAT Sources (2FHL,
$>50$~ GeV) catalog as well, obtaining $\sim (2-3)\sigma$ (pre-trial)
correlation, however the significance of correlation increases with higher
cutoff energy in the HESE sample for this case. We also fit available gamma-ray
data from these sources using a $pp$ interaction model and calculate expected
neutrino fluxes. We find that the expected neutrino fluxes for most of the
sources are at least an order of magnitude lower than the fluxes required to
produce the HESE neutrinos from these sources. This puts the starburst sources
being the origin of the IceCube HESE neutrinos in question.
