Stochastic classification models

Abstract

Two families of stochastic processes are constructed that are intended for use in classification problems where the aim is to classify units or specimens or species on the basis of measured features. The first model is an exchangeable cluster process generated by a standard Dirichlet allocation scheme. The set of classes is not pre-specified, so a new unit may be assigned to a previously unobserved class. The second model, which is more flexible, uses a marked point process as the mechanism generating the units or events, each with its associated class and feature. The conditional distribution given the superposition process is obtained in closed form for one particular marked point process. This distribution determines the conditional class probabilities, and thus the prediction rule for subsequent units.