Universal Outlier Hypothesis Testing: Application To Anomaly Detection

In outlier hypothesis testing, multiple observation sequences are collected, a small subset of which are outliers. Observations in an outlier sequence are generated by a mechanism different from that generating the observations in the majority of sequences. The goal is to best discern all the outlier sequences without any knowledge of the underlying generating mechanisms. A generalized likelihood test is considered in the fixed sample size setting. In the sequential setting, a test based on the Multihypothesis Sequential Probability Ratio Test and the repeated significance test is considered. The sequential test outperforms the generalized likelihood test when the lengths of the observation sequences exceed certain values. Applied to a real data set for spam detection, the performance of the proposed tests is shown to be superior to those based on the maximum mean discrepancy for large sample size.