  Online anomaly detection of time-series data is an important and challenging
task in machine learning. Gaussian processes (GPs) are powerful and flexible
models for modeling time-series data. However, the high time complexity of GPs
limits their applications in online anomaly detection. Attributed to some
internal or external changes, concept drift usually occurs in time-series data,
where the characteristics of data and meanings of abnormal behaviors alter over
time. Online anomaly detection methods should have the ability to adapt to
concept drift. Motivated by the above facts, this paper proposes the method of
sparse Gaussian processes with Q-function (SGP-Q). The SGP-Q employs sparse
Gaussian processes (SGPs) whose time complexity is lower than that of GPs, thus
significantly speeding up online anomaly detection. By using Q-function
properly, the SGP-Q can adapt to concept drift well. Moreover, the SGP-Q makes
use of few abnormal data in the training data by its strategy of updating
training data, resulting in more accurate sparse Gaussian process regression
models and better anomaly detection results. We evaluate the SGP-Q on various
artificial and real-world datasets. Experimental results validate the
effectiveness of the SGP-Q.
