Anomaly detection

In anomaly detection, we want to identify sequences that are notably different from the rest of the series. Anomalies or outliers can sometimes be the result of measurement error or noise, but they could indicate changes to behavior or aberrant behavior in the system under observation, which could require urgent action.

An important application of anomaly detection is automatic real-time monitoring of potentially complex, high-dimensional datasets.

It's time for an attempt at a definition (after D.M. Hawkins, 1980, "Identification of Outliers"):

Definition: An outlier is a data point that deviates so significantly from other observations that it could have been generated by a different mechanism.

Let's start with a plot, so we can see how an anomaly might look graphically. This will also provide us context for our discussion.

Anomaly detection methods can be distinguished between univariate and multivariate methods. Parametric...