Nearest Neighbour Classification with Monotonicity Constraints

In many application areas of machine learning, prior knowledge concerning the monotonicity of relations between the response variable and predictor variables is readily available. Monotonicity may also be an important model requirement with a view toward explaining and justifying decisions, such as acceptance/rejection decisions. We propose a modified nearest neighbour algorithm for the construction of monotone classifiers from data. We start by making the training data monotone with as few label changes as possible. The relabeled data set can be viewed as a monotone classifier that has the lowest possible error-rate on the training data. The relabeled data is subsequently used as the training sample by a modified nearest neighbour algorithm. This modified nearest neighbour rule produces predictions that are guaranteed to satisfy the monotonicity constraints. Hence, it is much more likely to be accepted by the intended users. Our experiments show that monotone kNN often outperforms standard kNN in problems where the monotonicity constraints are applicable.