Using negotiable features for prescription problems

Abstract

Data mining is usually concerned on the construction of accurate models from data, which are usually applied to well-defined problems that can be clearly isolated and formulated independently from other problems. Although much computational effort is devoted for their training and statistical evaluation, model deployment can also represent a scientific problem, when several data mining models have to be used together, constraints appear on their application, or they have to be included in decision processes based on different rules, equations and constraints. In this paper we address the problem of combining several data mining models for objects and individuals in a common scenario, where not only we can affect decisions as the result of a change in one or more data mining models, but we have to solve several optimisation problems, such as choosing one or more inputs to get the best overall result, or readjusting probabilities after a failure. We illustrate the point in the area of customer relationship management (CRM), where we deal with the general problem of prescription between products and customers. We introduce the concept of negotiable feature, which leads to an extended taxonomy of CRM problems of greater complexity, since each new negotiable feature implies a new degree of freedom. In this context, we introduce several new problems and techniques, such as data mining model inversion (by ranging on the inputs or by changing classification problems into regression problems by function inversion), expected profit estimation and curves, global optimisation through a Monte Carlo method, and several negotiation strategies in order to solve this maximisation problem.