  The sources of the majority of the high-energy astrophysical neutrinos
observed with the IceCube neutrino telescope at the South Pole are unknown. So
far, only a gamma-ray blazar was compellingly associated with the emission of
high-energy neutrinos. In addition, several studies suggest that the neutrino
emission from the gamma-ray blazar population only accounts for a small
fraction of the total astrophysical neutrino flux. In this work we probe the
production of high-energy neutrinos in the cores of Active Galactic Nuclei
(AGN), induced by accelerated cosmic rays in the accretion disk region. We
present a likelihood analysis based on eight years of IceCube data, searching
for a cumulative neutrino signal from three AGN samples created for this work.
The neutrino emission is assumed to be proportional to the accretion disk
luminosity estimated from the soft X-ray flux. Next to the observed soft X-ray
flux, the objects for the three samples have been selected based on their radio
emission and infrared color properties. For the largest sample in this search,
an excess of high-energy neutrino events with respect to an isotropic
background of atmospheric and astrophysical neutrinos is found, corresponding
to a post-trial significance of 2.60$\sigma$. Assuming a power-law spectrum,
the best-fit spectral index is $2.03^{+0.14}_{-0.11}$, consistent with
expectations from particle acceleration in astrophysical sources. If
interpreted as a genuine signal with the assumptions of a proportionality of
X-ray and neutrino fluxes and a model for the sub-threshold flux distribution,
this observation implies that at 100 TeV, 27$\%$ - 100$\%$ of the observed
neutrinos arise from particle acceleration in the core of AGN.
