Summary
2020
Session Number:E01
Session:
Number:E01-3
Optimal Resolution of Change-Point Detection with Empirically Observed Statistics and Erasures
Haiyun He, Qiaosheng Zhang, Vincent Tan,
pp.582-586
Publication Date:2020/10/18
Online ISSN:2188-5079
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Summary:
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. 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.