An important subproblem in supervised tasks such as decision tree induction and subgroup discovery is finding an interesting binary feature (such as a node split or a subgroup refinement) based on a numeric or nominal attribute, with respect to some discrete or continuous target variable. Often one is faced with a trade-off between the expressiveness of such features on the one hand and the ability to efficiently traverse the feature search space on the other hand. In this article, we present efficient algorithms to mine binary features that optimize a given convex quality measure. For numeric attributes, we propose an algorithm that finds an optimal interval, whereas for nominal attributes, we give an algorithm that finds an optimal value set. By restricting the search to features that lie on a convex hull in a coverage space, we can significantly reduce computation time. We present some general theoretical results on the cardinality of convex hulls in coverage spaces of arbitrary dimensions and perform a complexity analysis of our algorithms. In the important case of a binary target, we show that these algorithms have linear runtime in the number of examples. We further provide algorithms for additive quality measures, which have linear runtime regardless of the target type. Additive measures are particularly relevant to feature discovery in subgroup discovery. Our algorithms are shown to perform well through experimentation and furthermore provide additional expressive power leading to higher-quality results.

The estimated total costs corrected for treatment gap were €1.15 to €1.64 billion. These results indicate room for improvement in the health care policy against osteoporosis.

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Abstract. Conventional techniques for detecting outliers address the problem of finding isolated observations that significantly differ from other observations that are stored in a database. For example, in the context of health insurance, one might be interested in finding unusual claims concerning prescribed medicines. Each claim record may contain information on the prescribed drug (its code), volume (e.g., the number of pills and their weight), dosing and the price. Finding outliers in such data can be used for identifying fraud. However, when searching for fraud, it is more important to analyse data not on the level of single records, but on the level of single patients, pharmacies or GP's.In this paper we present a novel approach for finding outliers in such hierarchical data. Our method uses standard techniques for measuring outlierness of single records and then aggregates these measurements to detect outliers in entities that are higher in the hierarchy. We applied this method to a set of about 40 million records from a health insurance company to identify suspicious pharmacies.