  Often, data contains only composite events composed of multiple events, some
observed and some unobserved. For example, search ad click is observed by a
brand, whereas which customers were shown a search ad - an actionable variable
- is often not observed. In such cases, inference is not possible on unobserved
event. This occurs when a marketing action is taken over earned and paid
digital channels. Similar setting arises in numerous datasets where multiple
actors interact. One approach is to use the composite event as a proxy for the
unobserved event of interest. However, this leads to invalid inference. This
paper takes a direct approach whereby an event of interest is identified based
on information on the composite event and aggregate data on composite events
(e.g. total number of search ads shown). This work contributes to the
literature by proving identification of the unobserved events' probabilities up
to a scalar factor under mild condition. We propose an approach to identify the
scalar factor by using aggregate data that is usually available from earned and
paid channels. The factor is identified by adding a loss term to the usual
cross-entropy loss. We validate the approach on three synthetic datasets. In
addition, the approach is validated on a real marketing problem where some
observed events are hidden from the algorithm for validation. The proposed
modification to the cross-entropy loss function improves the average
performance by 46%.
