A L1 Minimization Optimal Corrective Explanation Procedure for Probabilistic Databases

We propose to use a, recently introduced, efficient L1 distance minimization through mixed-integer linear programming for minimizing the number of valuations to be modified inside an incoherent probabilistic assessment. This is in line with one basic principle of optimal corrective explanation for decision makers. A shrewd use of constraints and of slack variables permit to steer the correction of incoherent assessments towards aimed directions, like e.g. the minimal number of changes. Such corrective explanations can be searched alone, as minimal changes, or jointly with the property of being also inside the L1 distance minimizers (in a bi-optimal point of view). The detection of such bi-optimal solutions can be performed efficiently by profiting from the geometric characterization of the whole set of L1 minimizers and from the properties of L1 topology.