Global tests for novelty

Outlier detection covers the wide range of methods aiming at identifying observations that are considered unusual. Novelty detection, on the other hand, seeks observations among newly generated test data that are exceptional compared with previously observed training data. In many applications, the general existence of novelty is of more interest than identifying the individual novel observations. For instance, in high-throughput cancer treatment screening experiments, it is meaningful to test whether any new treatment effects are seen compared with existing compounds. Here, we present hypothesis tests for such global level novelty. The problem is approached through a set of very general assumptions, making it innovative in relation to the current literature. We introduce test statistics capable of detecting novelty. They operate on local neighborhoods and their null distribution is obtained by the permutation principle. We show that they are valid and able to find different types of novelty, e.g. location and scale alternatives. The performance of the methods is assessed with simulations and with applications to real data sets.

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