The Inverse Bagging Algorithm: Anomaly Detection by Inverse Bootstrap Aggregating

For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it) consists in avoiding to modify the kinematic distributions of the well modeled one. A bootstrap technique is used to identify sub-samples rich in the well modeled process, and classify each event according to the frequency of it being part of such sub-samples. Comparisons with general MVA algorithms will be shown, as well as a study of the asymptotic properties of the method, making use of a public domain data set that models a typical search for new physics as performed at hadronic colliders such as the Large Hadron Collider (LHC). The most popular classification algorithms based on supervised learning require a well modeled signal and a well modeled background. For the classifier to learn how to separate the two classes, it is crucial that both models are known. The case in which either signal or background has an unknown PDF is, however, acquiring importance in many classification problems that arise in the realm of particle physics, due to the fact that every passing day more and more known models are ruled out by the data. Two scenarios are mainly interesting for particle physics: a very well known background modeled from simulation, in presence of an unknown rare signal; a very well known signal modeled from simulation, contaminated by a background of origin unclear and/or not simulable. In both scenarios, it is desirable to manipulate the fraction of the unknown process, without modifying the kinematic distributions of the very well known one.