Online Anomaly Detection with Sparse Gaussian Processes

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.