Reducing sequential change detection to sequential estimation
This provides a method for detecting changes in data streams with strong guarantees, applicable to dependent observations and nonparametric distributions, but it is incremental as it builds on prior reductions and e-detectors.
The paper tackles the problem of sequential change detection by reducing it to sequential estimation using confidence sequences, achieving an average run length of at least 1/α with minimal structural assumptions.
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $θ$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-α)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/α$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).