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This paper investigates a novel offline change-point detection problem froman information-theoretic perspective. In contrast to most related works, weassume that the knowledge of the underlying pre- and post-change distributionsare not known and can only be learned from the training sequences which areavailable. We further require the probability of the \emph{estimation error} todecay either exponentially or sub-exponentially fast (correspondingrespectively to the large and moderate deviations regimes in information theoryparlance). Based on the training sequences as well as the test sequenceconsisting of a single change-point, we design a change-point estimator andfurther show that this estimator is optimal by establishing matching (strong)converses. This leads to a full characterization of the optimal confidencewidth (i.e., half the width of the confidence interval within which the truechange-point is located at with high probability) as a function of theundetected error, under both the large and moderate deviations regimes.

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