Novelty detection using extreme value statistics

TLDR

Extreme value theory studies the tails of distributions and is applied to novelty detection by flagging points that lie outside expected extreme ranges, though current methods often rely on heuristic thresholds. The study demonstrates that extreme value statistics provide a principled alternative to heuristic thresholds for novelty detection.

Abstract

Extreme value theory is a branch of statistics that concerns the distribution of data of unusually low or high value, i.e. in the tails of some distribution. These extremal points are important in many applications as they represent the outlying regions of normal events against which we may wish to define abnormal events. In the context of density modelling, novelty detection or radial-basis function systems, points that lie outside of the range of expected extreme values may be flagged as outliers. There has been interest in the area of novelty detection, but decisions as to whether a point is an outlier or not tend to be made on the basis of exceeding some (heuristic) threshold. It is shown that a more principled approach may be taken using extreme value statistics.