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On Anomaly Ranking and Excess-Mass Curves

Abstract : Learning how to rank multivariate unlabeled observations depending on their degree of ab-normality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be considered as abnormal. In the 1-d situation, measurements are generally considered as "abnormal" when they are remote from central measures such as the mean or the median. Anomaly detection then relies on tail analysis of the variable of interest. Extensions to the multivariate setting are far from straightforward and it is precisely the main purpose of this paper to introduce a novel and convenient (functional) criterion for measuring the performance of a scoring function regarding the anomaly ranking task, referred to as the Excess-Mass curve (EM curve). In addition, an adaptive algorithm for building a scoring function based on un-labeled data X 1 ,. .. , X n with a nearly optimal EM is proposed and is analyzed from a statistical perspective.
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Nicolas Goix, Anne Sabourin, Stéphan Clémençon. On Anomaly Ranking and Excess-Mass Curves. On Anomaly Ranking and Excess-Mass Curves, pp.287-295, 2015. ⟨hal-02107450⟩

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