Changepoint Detection in the Presence of Outliers
This addresses the challenge of online changepoint detection in noisy real-world applications like well-log analysis and copy number variation detection, though it is incremental as it adapts existing penalised cost methods.
The paper tackles the problem of changepoint detection in data with outliers or heavy-tailed noise, which can cause traditional methods to infer false changepoints, by proposing a robust approach using bounded loss functions like the biweight loss, resulting in consistent estimation of changepoint numbers and accurate location estimates.
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 difficult for 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 loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitable -- as we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can 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 show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analysing well-log data, detecting copy number variation, and detecting tampering of wireless devices.