  We present the study on the relationship between SMBHs and their host
galaxies using our variability-selected AGN sample ($i_\mathrm{AB} \leq 25.9,\
z \leq 4.5$) constructed from the HSC-SSP Ultra-deep survey in the COSMOS
field. We estimated the BH mass ($M_\mathrm{BH}=10^{5.5-10}\ M_{\odot}$) based
on the single-epoch virial method and the total stellar mass
($M_\mathrm{star}=10^{10-12}\ M_{\odot}$) by separating the AGN component with
SED fitting. We found that the redshift evolution of the BH-stellar mass ratio
($M_\mathrm{BH}/M_\mathrm{star}$) depends on the $M_\mathrm{BH}$ which is
caused by the no significant correlation between $M_\mathrm{BH}$ and
$M_\mathrm{star}$. Variable AGNs with massive SMBHs ($M_\mathrm{BH}>10^{9}\
M_{\odot}$) at $1.5<z<3$ show considerably higher BH-stellar mass ratios
($>\sim1\%$) than the BH-bulge ratios ($M_\mathrm{BH}/M_\mathrm{bulge}$)
observed in the local universe for the same BH range. This implies that there
is a typical growth path of massive SMBHs which is faster than the formation of
the bulge component as final products seen in the present day. For the low-mass
SMBHs ($M_\mathrm{BH}<10^{8}\ M_{\odot}$) at $0.5<z<3$, on the other hand,
variable AGNs show the similar BH-stellar mass ratios with the local objects
($\sim 0.1\%$) but smaller than those observed at $z > 4$. We interpret that
host galaxies harboring less massive SMBHs at intermediate redshift have
already acquired sufficient stellar mass, although high-z galaxies are still in
the early stage of galaxy formation relative to those at the intermediate/local
universe.
