A least-squares approach to anomaly detection in static and sequential data

• We present a novel, probabilistic, nonparametric least-squares method for anomaly detection.
• A hidden Markov model framework is incorporated for anomaly detection in sequences.
• The method is faster at training and test time on large datasets than popular alternative methods.

We describe a probabilistic, nonparametric method for anomaly detection, based on a squared-loss objective function which has a simple analytical solution. The method emerges from extending recent work in nonparametric least-squares classification to include a “none-of-the-above” class which models anomalies in terms of non-anamalous training data. The method shares the flexibility of other kernel-based anomaly detection methods, yet is typically much faster to train and test. It can also be used to distinguish between multiple inlier classes and anomalies. The probabilistic nature of the output makes it straightforward to apply even when test data has structural dependencies; we show how a hidden Markov model framework can be incorporated in order to identify anomalous subsequences in a test sequence. Empirical results on datasets from several domains show the method to have comparable discriminative performance to popular alternatives, but with a clear speed advantage.