  We study galaxy mass assembly and cosmic star formation rate (SFR) at
high-redshift (z$\gt$4), by comparing data from multiwavelength surveys with
predictions from the GAlaxy Evolution and Assembly (GAEA) model. GAEA
implements a stellar feedback scheme partially based on cosmological
hydrodynamical simulations, that features strong stellar driven outflows and
mass-dependent timescale for the re-accretion of ejected gas. In previous work,
we have shown that this scheme is able to correctly reproduce the evolution of
the galaxy stellar mass function (GSMF) up to $z\sim3$. We contrast model
predictions with both rest-frame Ultra-Violet (UV) and optical luminosity
functions (LF), which are mostly sensible to the SFR and stellar mass,
respectively. We show that GAEA is able to reproduce the shape and redshift
evolution of both sets of LFs. We study the impact of dust on the predicted LFs
and we find that the required level of dust attenuation is in qualitative
agreement with recent estimates based on the UV continuum slope. The
consistency between data and model predictions holds for the redshift evolution
of the physical quantities well beyond the redshift range considered for the
calibration of the original model. In particular, we show that GAEA is able to
recover the evolution of the GSMF up to z$\sim$7 and the cosmic SFR density up
to z$\sim$10.
