Optimal Change-Point Detection with Training Sequences in the Large and Moderate Deviations Regimes

• URL: http://arxiv.org/abs/2003.06511v4
• Date: Sun, 3 Oct 2021 04:51:27 GMT
• Title: Optimal Change-Point Detection with Training Sequences in the Large and Moderate Deviations Regimes
• Authors: Haiyun He, Qiaosheng Zhang, and Vincent Y. F. Tan
• Abstract summary: This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. We assume that the knowledge of the underlying pre- and post-change distributions are not known and can only be learned from the training sequences which are available.
• Score: 72.68201611113673
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not known and can only be learned from the training sequences which are available. We further require the probability of the \emph{estimation error} to decay either exponentially or sub-exponentially fast (corresponding respectively to the large and moderate deviations regimes in information theory parlance). Based on the training sequences as well as the test sequence consisting of a single change-point, we design a change-point estimator and further show that this estimator is optimal by establishing matching (strong) converses. This leads to a full characterization of the optimal confidence width (i.e., half the width of the confidence interval within which the true change-point is located at with high probability) as a function of the undetected error, under both the large and moderate deviations regimes.

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