Speaker
Description
Weakly-supervised anomaly searches, such as CWOLA and CATHODE, typically train a classifier to separate a signal region from a sideband-estimate background and then cut on the classifier output to create a signal-enriched dataset. We show that there is a more efficient use of the output: the same classifier output can be used instead as a per-event weight, This results in a more powerful test with no cuts and significantly fewer discarded events. We formulate the anomaly detection problem as a hypothesis test over a scaled Poisson likelihood, and we show how to extract a profile-likelihood test statistic that is consistent with Wilks' Theorem under the null hypothesis, allowing for the precise extraction of meaningful $p$-values. We also provide theoretical estimates for the power of the weakly supervised anomaly detection tests, both traditional and weighted, placing the study of the statistical properties of anomaly detection on firmer theoretical ground. This weights method can be easily applied to any existing weakly supervised anomaly detection search for free, with no additional training or calibration required.