Log In Sign Up

On Anomaly Ranking and Excess-Mass Curves

by   Nicolas Goix, et al.

Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/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 unlabeled data X1 , . . . , Xn with a nearly optimal EM is proposed and is analyzed from a statistical perspective.


page 1

page 2

page 3

page 4


Mass Volume Curves and Anomaly Ranking

This paper aims at formulating the issue of ranking multivariate unlabel...

Ranking Data with Continuous Labels through Oriented Recursive Partitions

We formulate a supervised learning problem, referred to as continuous ra...

Functional Isolation Forest

For the purpose of monitoring the behavior of complex infrastructures (e...

Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Ranking

The ROC curve is the gold standard for measuring the performance of a te...

Learning to Rank Anomalies: Scalar Performance Criteria and Maximization of Two-Sample Rank Statistics

The ability to collect and store ever more massive databases has been ac...

How to Evaluate the Quality of Unsupervised Anomaly Detection Algorithms?

When sufficient labeled data are available, classical criteria based on ...

Binomial Tails for Community Analysis

An important task of community discovery in networks is assessing signif...