Sequential Changepoint Detection via Backward Confidence Sequences
Shubhanshu Shekhar,u00a0Aaditya Ramdas
We present a simple reduction from sequential estimation to sequential changepoint detection (SCD). In short, suppose we are interested in detecting changepoints in some parameter or functional $ heta$ of the underlying distribution. We demonstrate that if we can construct a confidence sequence (CS) for $ heta$, then we can also successfully perform SCD for $ heta$. This is accomplished by checking if two CSs u2014 one forwards and the other backwards u2014 ever fail to intersect. Since the literature on CSs has been rapidly evolving recently, the reduction provided in this paper immediately solves several old and new change detection problems. Further, our u201cbackward CSu201d, constructed by reversing time, is new and potentially of independent interest. We provide strong nonasymptotic guarantees on the frequency of false alarms and detection delay, and demonstrate numerical effectiveness on several problems.
