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Optimal Resolution of Change-Point Detection with Empirically Observed Statistics

13 March 2020
Haiyun He
Q. Zhang
Vincent Y. F. Tan
ArXiv (abs)PDFHTML
Abstract

This paper revisits the offline change-point detection problem from a statistical learning perspective. Instead of assuming that the underlying pre- and post-change distributions are known, it is assumed that we have partial knowledge of these distributions based on empirically observed statistics in the form of training sequences. Our problem formulation finds a variety of real-life applications from detecting when climate change occurred to detecting when a virus mutated. Using the training sequences as well as the test sequence consisting of a single-change and allowing for the erasure or rejection option, we derive the optimal resolution between the estimated and true change-points under two different asymptotic regimes on the undetected error probability -- namely, the large and moderate deviations regimes. In both regimes, strong converses are also proved. In the moderate deviations case, the optimal resolution is a simple function of a symmetrized version of the chi-square distance.

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