Systems and methods are provided for matching one or more first entities with one or more of second entities. Factor graph representations of the first entities and a plurality of second entities are stored. The factor graph representation of the plurality of second entities includes an identity variable referencing each of the individual second entities. When a request is received from a requesting one of the first set of entities for a match from the second set of entities, the first factor graph and the second factor graph are merged, and the merged graph is solved for a probability mass function for the identity variable to yield a probability vector to be used to identify those ones of the plurality of second entities having the highest probabilities as matches to be returned in response to the request.