  We study quark and gluon jets separately using public collider data from the
CMS experiment. Our analysis is based on 2.3/fb of proton-proton collisions at
7 TeV, collected at the Large Hadron Collider in 2011. We define two
non-overlapping samples via a pseudorapidity cut -- central jets with |eta| <
0.65 and forward jets with |eta| > 0.65 -- and employ jet topic modeling to
extract individual distributions for the maximally separable categories. Under
certain assumptions, such as sample independence and mutual irreducibility,
these categories correspond to "quark" and "gluon" jets, as given by a recently
proposed operational definition. We consider a number of different methods for
extracting reducibility factors from the central and forward datasets, from
which the fractions of quark jets in each sample can be determined. The
greatest stability and robustness to statistical uncertainties is achieved by a
novel method based on parametrizing the endpoints of a receiver operating
characteristic (ROC) curve. To mitigate detector effects, which would otherwise
induce unphysical differences between central and forward jets, we use the
OmniFold method to perform central value unfolding. As a demonstration of the
power of this method, we extract the intrinsic dimensionality of the quark and
gluon jet samples, which exhibit Casimir scaling, as expected from the
strongly-ordered limit. To our knowledge, this work is the first application of
full phase space unfolding to real collider data, and one of the first
applications of topic modeling to extract separate quark and gluon
distributions at the LHC.
