A survey on ROC-based ordinal regression

Abstract

Ordinal regression can be seen as a special case of preference learning, in which the class labels corresponding with data instances can take values from an ordered finite set. In such a setting, the classes usually have a linguistic interpretation attached by humans to subdivide the data into a number of preference bins. In this chapter, we give a general survey on ordinal regression from a machine learning point of view. In particular, we elaborate on some important connections with ROC analysis that have been introduced recently by the present authors. First, the important role of an underlying ranking function in ordinal regression models is discussed, as well as its impact on the performance evaluation of such models. Subsequently, we describe a new ROC-based performance measure that directly evaluates the underlying ranking function, and we place it in the more general context of ROC analysis as the volume under an r-dimensional ROC surface (VUS) for in general rclasses. Furthermore, we also discuss the scalability of this measure and show that it can be computed very efficiently for large samples. Finally, we present a kernel-based learning algorithm that optimizes VUS as a specific case of structured support vector machines. © 2011 Springer-Verlag Berlin Heidelberg.