| It is widely recognized that in learning prediction models from data, the use of relevant prior knowledge may drastically improve their performance. A frequently available form of prior knowledge in many application areas concerns the monotonicity of relations between the response variable and predictor variables. Monotonicity may also be an important model requirement with a view toward explaining and justifying decisions, such as acceptance/rejection decisions. We propose a {\em nonparametric} approach to the construction of monotone classifiers from data. The reason for this choice is that we don't want to impose any additional constraints beyond monotonicity. As a consequence the results of our work will be applicable to a broad range of problems. The starting point of the proposed research is an efficient algorithm to make nonmonotone data sets monotone with as few label changes as possible. The relabeled data set can be viewed as the monotone classifier that has the lowest possible error-rate on the training data. This classifier is however only defined on the observed data points. Hence, the classifier has to be extended to the entire input space in such a way that the monotonicity constraints are satisfied, and the observed data points are used in an optimal way to classify new cases. Another important issue, is the minimization of different loss functions. For example, the minimization of total misclassification costs is of considerable interest, since it is reasonable to assume that misclassification costs will differ in case of ordered class labels. |
