In many applications of data mining it is known beforehand that the response variable should be increasing (or decreasing) in the attributes. We propose two algorithms to exploit such monotonicity constraints for active learning in ordinal classification in two different settings. The basis of our approach is the observation that if the class label of an object is given, then the monotonicity constraints may allow the labels of other objects to be inferred. For instance, from knowing that loan applicant a is rejected, it can be concluded that all applicants that score worse than a on all criteria should be rejected as well. We propose two heuristics to select good query points. These heuristics make a selection based on a point's potential to determine the labels of other points. The algorithms, each implemented with the proposed heuristics, are evaluated on artificial and real data sets to study their performance. We conclude that exploitation of monotonicity constraints can be very beneficial in active learning.

We describe a monotone classification algorithm called MOCA that attempts to minimize the mean absolute prediction error for classification problems with ordered class labels.We first find a monotone classifier with minimum L1loss on the training sample, and then use a simple interpolation scheme to predict the class labels for attribute vectors not present in the training data.We compare MOCA to the ordinal stochastic dominance learner (OSDL), on artificial as well as real data sets. We show that MOCA often outperforms OSDL with respect to mean absolute prediction error.