Data-adaptive symmetric CUSUM for sequential change detection

Detecting change points sequentially in a streaming setting, especially when both the mean and the variance of the signal can change, is often a challenging task. A key difficulty in this context often involves setting an appropriate detection threshold, which for many standard change statistics may need to be tuned depending on the prechange and postchange distributions. This presents a challenge in a sequential change detection setting when a signal switches between multiple distributions. Unfortunately, change point detection schemes that use the log-likelihood ratio, such as cumulative sum (CUSUM) and the generalized log-likelihood ratio (GLR), are quick to react to changes but are not symmetric when both the mean and the variance of the signal change. This makes it difficult to set a single threshold to detect multiple change points sequentially in a streaming setting. We propose a modified version of CUSUM that we call data-adaptive symmetric CUSUM (DAS-CUSUM). The DAS-CUSUM procedure is symmetric for changes between distributions, making it suitable to set a single threshold to detect multiple change points sequentially in a streaming setting. We provide results that relate the expected detection delay and average run length for our proposed procedure when both prechange and postchange distributions are normally distributed. Experiments on simulated and real-world data show the utility of DAS-CUSUM.