A multi-instance deep neural network classifier: application to Higgs boson CP measurement

We investigate properties of a classifier applied to the measurements of the CP state of the Higgs boson in $H\rightarrow\tau\tau$ decays. The problem is framed as binary classifier applied to individual instances. Then the prior knowledge that the instances belong to the same class is used to define the multi-instance classifier. Its final score is calculated as multiplication of single instance scores for a given series of instances. In the paper we discuss properties of such classifier, notably its dependence on the number of instances in the series. This classifier exhibits very strong random dependence on the number of epochs used for training and requires careful tuning of the classification threshold. We derive formula for this optimal threshold.