Abstract. 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.

Abstract. In most databases, it is possible to identify small partitions of the data where the observed distribution is notably different from that of the database as a whole. In classical subgroup discovery, one considers the distribution of a single nominal attribute, and exceptional subgroups show a surprising increase in the occurrence of one of its values. In this paper, we introduce Exceptional Model Mining (EMM), a framework that allows for more complicated target concepts. Rather than finding subgroups based on the distribution of a single target attribute, EMM finds subgroups where a model fitted to that subgroup is somehow exceptional. We discuss regression as well as classification models, and define quality measures that determine how exceptional a given model on a subgroup is. Our framework is general enough to be applied to many types of models, even from other paradigms such as association analysis and graphical modeling.

Whenever a dataset has multiple discrete target variables, we want our algorithms to consider not only the variables themselves, but also the interdependencies between them. We propose to use these interdependencies to quantify the quality of subgroups, by integrating Bayesian networks with the Exceptional Model Mining framework. Within this framework, candidate subgroups are generated. For each candidate, we fit a Bayesian network on the target variables. Then we compare the network's structure to the structure of the Bayesian network fitted on the whole dataset. To perform this comparison, we define an edit distance-based distance metric that is appropriate for Bayesian networks. We show interesting subgroups that we experimentally found with our method on datasets from music theory, semantic scene classification, biology and zoogeography.

Therapeutic, IV.

No abstract