Changepoint Detection in the Presence of Outliers

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints in order to fit the outliers. To overcome this problem, data often needs to be pre-processed to remove outliers, though this is not feasible in applications where the data needs to be analysed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalised cost approaches for detecting changes so that they use cost functions that are less sensitive to outliers. We argue that cost functions that are bounded, such as the classical biweight cost, are particularly suitable -- as we show that only bounded cost functions are robust to arbitrarily extreme outliers. We present a novel and efficient dynamic programming algorithm that can then find the optimal segmentation under our penalised cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analysed online. We present theoretical bounds on the worst-case complexity of this algorithm, and show empirically that its average computational cost is linear in the amount of the data. We show the usefulness of our approach for applications such as analysing well-log data, detecting copy number variation, and detecting tampering of wireless devices.