  We study the problem of data-driven background estimation, arising in the
search of physics signals predicted by the Standard Model at the Large Hadron
Collider. Our work is motivated by the search for the production of pairs of
Higgs bosons decaying into four bottom quarks. A number of other physical
processes, known as background, also share the same final state. The data
arising in this problem is therefore a mixture of unlabeled background and
signal events, and the primary aim of the analysis is to determine whether the
proportion of unlabeled signal events is nonzero. A challenging but necessary
first step is to estimate the distribution of background events. Past work in
this area has determined regions of the space of collider events where signal
is unlikely to appear, and where the background distribution is therefore
identifiable. The background distribution can be estimated in these regions,
and extrapolated into the region of primary interest using transfer learning
with a multivariate classifier. We build upon this existing approach in two
ways. First, we revisit this method by developing a customized residual neural
network which is tailored to the structure and symmetries of collider data.
Second, we develop a new method for background estimation, based on the optimal
transport problem, which relies on modeling assumptions distinct from earlier
work. These two methods can serve as cross-checks for each other in particle
physics analyses, due to the complementarity of their underlying assumptions.
We compare their performance on simulated double Higgs boson data.
