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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 pre-change and post-change distributions. This presents a challenge in a sequential change detection setting when a signal switches between multiple distributions. For example, consider a signal where change points are indicated by increases/decreases in the mean and variance of the signal. In this context, we would like to be able to compare our change statistic to a ﬁxed threshold that will be symmetric to either increases or decreases in the mean and variance. Unfortunately, change point detection schemes that use the log-likelihood ratio, such as CUSUM and 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 change point detection 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 to the expected detection delay and average run length for our proposed procedure. Extensive simulations are used to validate these results. Experiments on real-world data further show the utility of using DAS-CUSUM over both CUSUM and GLR.