A Bayesian approach for on-line max and min auditing

In this paper we consider the on-line max and min query auditing problem: given a private association between fields in a data set, a sequence of max and min queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max and min queries, without "no duplicates" assumption, can be audited by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.