  The different modifications of quark- and gluon-initiated jets in the
quark-gluon plasma (QGP) produced in heavy-ion collisions is a long-standing
question that has not yet received a definitive answer from experiments. In
particular, the relative sizes of the modification of quark and gluon jets
differ between theoretical models. Therefore, a fully data-driven technique is
crucial for an unbiased extraction of the quark and gluon jet spectra and
substructure. We perform a proof-of-concept study based on proton-proton and
heavy-ion collision events from the \textsc{Pyquen} generator with statistics
accessible in Run 4 of the Large Hadron Collider. We use a statistical
technique called topic modeling to separate quark and gluon contributions to
jet observables. We demonstrate that jet substructure observables, such as the
jet shape and jet fragmentation function, can be extracted using this
data-driven method. These values can then be used to obtain the modification of
quark and gluon jet substructures in the QGP. We also perform the topic
separation on smeared input data to demonstrate that the approach is robust to
fluctuations arising from a QGP background. These results suggest the potential
for an experimental determination of quark and gluon jet spectra and their
substructure.
