  Ultra-luminous infrared galaxies (ULIRGs) have infrared luminosities
$L_{\mathrm{IR}} \geq 10^{12} L_{\odot}$, making them the most luminous objects
in the infrared sky. These dusty objects are generally powered by starbursts
with star-formation rates that exceed $100~ M_{\odot}~ \mathrm{yr}^{-1}$,
possibly combined with a contribution from an active galactic nucleus. Such
environments make ULIRGs plausible sources of astrophysical high-energy
neutrinos, which can be observed by the IceCube Neutrino Observatory at the
South Pole. We present a stacking search for high-energy neutrinos from a
representative sample of 75 ULIRGs with redshift $z \leq 0.13$ using 7.5 years
of IceCube data. The results are consistent with a background-only observation,
yielding upper limits on the neutrino flux from these 75 ULIRGs. For an
unbroken $E^{-2.5}$ power-law spectrum, we report an upper limit on the stacked
flux $\Phi_{\nu_\mu + \bar{\nu}_\mu}^{90\%} = 3.24 \times 10^{-14}~
\mathrm{TeV^{-1}~ cm^{-2}~ s^{-1}}~ (E/10~ \mathrm{TeV})^{-2.5}$ at 90%
confidence level. In addition, we constrain the contribution of the ULIRG
source population to the observed diffuse astrophysical neutrino flux as well
as model predictions.
