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

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 underlying pre- and post-change distributions are not known can only be learned training sequences which available. We further require probability estimation error decay either exponentially or sub-exponentially fast (corresponding respectively large moderate deviations regimes in information theory parlance). Based on as well test sequence consisting single change-point, design estimator show this is optimal by establishing matching (strong) converses. leads full characterization confidence width (i.e., half interval within true located at with high probability) function undetected error, under both regimes.