Neural Autoregressive Flows for Data-driven background estimation as demonstrated in a search for four-top quark production in the all-hadronic final state with CMS at 13 TeV

A novel machine-learning based background estimation technique using normalizing flows in order to estimate background distributions from data in control regions is described in detail. This is demonstrated in four-top quark production in the all hadronic channel in Run II (TOP-21-005), which was facilitated for the first time through the ability of this method to estimate dominant QCD multijets and tt ̄ backgrounds. The flow is able to reliably estimate the distribution of complex variables in signal regions by learning the transformation from input simulated distributions to target data distributions in control regions inspired by the "ABCD" method. This "ABCDnn" method as applied to the four-top all hadronic method is described, including discussion of selections and choice of control regions, validation of the method, estimation of uncertainties, and discussion of closure tests. A public git repository for training the network is also included. This background estimation method is applicable to other hadronic-dominated analyses where QCD multijets simulation is unreliable or statistically limited. This work is part of an ongoing paper (MLG-23-004) and is expected to be included in an anticipated Run 3 iteration of the all hadronic four-top analysis.