Cost-Based Quality Measures in Subgroup Discovery

Abstract

In this paper we consider data where examples are not only labeled in the classical sense (positive or negative), but also have costs associated with them. In this sense, each example has two target attributes, and we aim to find clearly defined subsets of the data where the values of these two targets have an unusual distribution. In other words, we are focusing on a Subgroup Discovery task over somewhat unusual data, and investigate possible quality measures that take into account both the binary as well as the cost target. In defining such quality measures, we aim to produce interpretable valuation of subgroups, such that data analysts can directly value the findings, and relate these to monetary gains or losses. Our work is particularly relevant in the domain of health care fraud detection. In this data, the binary target identifies the patients of a specific medical practitioner under investigation, whereas the cost target specifies how much money is spent on each patient. When looking for clear specifications of differences in claim behavior, we clearly need to take into account both the ‘positive’ examples (patients of the practitioner) and ‘negative’ examples (other patients), as well as information about costs of all patients. A typical subgroup will now list a number of treatments, and how the patients of our practitioner differ in both the prevalence of the treatments as well as the associated costs. An additional angle considered in this paper is the recently proposed Local Subgroup Discovery, where subgroups are judged according to the difference with a local reference group, rather than the entire dataset. We show how the cost-based analysis of data specifically fits this local focus.