Statistical Approach to Ordinal Classification with Monotonicity Constraints

In the ordinal classification with monotonicity constraints, it is assumed that the class label of an object does not decrease when evaluations of this object on considered attributes increase. In this paper, we formulate the problem of ordinal classification with monotonicity constraints from statistical point of view, by imposing constraints both on the probability distribution and on the loss function. We propose a procedure for “monotonizing” the data by relabeling objects, based on minimization of the empirical risk in the class of all monotone functions. The procedure is then used as a preprocessing tool, improving the accuracy of the classifiers. We verify these claims in a computational experiment.