Generalized Statistical Methods for Unsupervised Minority Class Detection in Mixed Data Sets

Minority class detection is the problem of detecting the occurrence of rare key events differing from the majority of a data set. This paper considers the problem of unsupervised minority class detection for multidimensional data that are highly nongaussian, mixed (continuous and/or discrete), noisy, and nonlinearly related, such as occurs, for example, in fraud detection in typical financial data. A statistical modeling approach is proposed which is a subclass of graphical model techniques. It exploits the properties of exponential family distributions and generalizes techniques from classical linear statistics into a framework referred to as Generalized Linear Statistics (GLS). The methodology exploits the split between the data space and the parameter space for exponential family distributions and solves a nonlinear problem by using classical linear statistical tools applied to data that has been mapped into the parameter space. A fraud detection technique utilizing low-dimensional information learned by using an Iteratively Reweighted Least Squares (IRLS) based approach to GLS is proposed in the parameter space for data of mixed type. ROC curves for an initial simulation on synthetic data are presented, which gives predictions for results on actual financial data sets.