Universal quickest outlier detection and isolation

Quickest outlier detection and isolation is studied in universal settings. Initially, multiple data streams are commonly distributed according to a “typical” distribution. At the change time, an outlier stream emerges and starts to be distributed according to the “outlier” distribution, while the rest of the streams remain to be distributed according to the typical one. Two tests are proposed to quickly isolate the outlier. The first test is shown to be asymptotically optimal universally when only the typical distribution is known, and in the limit of the large number of streams when neither the outlier nor typical distribution is known. The performance of the second test, which is more practical, is also characterized.