  We propose a general framework leveraging the halo-galaxy connection to link
galaxies observed at different redshift in a statistical way, and use the link
to infer the redshift evolution of the galaxy population. Our tests based on
hydrodynamic simulations show that our method can accurately recover the
stellar mass assembly histories up to $z\sim 3$ for present star-forming and
quiescent galaxies down to $10^{10}h^{-1}M_{\odot}$. Applying the method to
observational data shows that the stellar mass evolution of the main
progenitors of galaxies depends strongly on the properties of descendants, such
as stellar mass, halo mass, and star formation states. Galaxies hosted by
low-mass groups/halos at the present time have since $z\sim 1.8$ grown their
stellar mass $\sim 2.5$ times as fast as those hosted by massive clusters. This
dependence on host halo mass becomes much weaker for descendant galaxies with
similar star formation states. Star-forming galaxies grow about 2-4 times
faster than their quiescent counterparts since $z\sim 1.8$. Both TNG and EAGLE
simulations over-predict the progenitor stellar mass at $z>1$, particularly for
low-mass descendants.
