  Accurately detecting multiple change-points is critical for various
applications, but determining the optimal number of change-points remains a
challenge. Existing approaches based on information criteria attempt to balance
goodness-of-fit and model complexity, but their performance varies depending on
the model. Recently, data-driven selection criteria based on cross-validation
has been proposed, but these methods can be prone to slight overfitting in
finite samples. In this paper, we introduce a method that controls the
probability of overestimation and provides uncertainty quantification for
learning multiple change-points via cross-validation. We frame this problem as
a sequence of model comparison problems and leverage high-dimensional
inferential procedures. We demonstrate the effectiveness of our approach
through experiments on finite-sample data, showing superior uncertainty
quantification for overestimation compared to existing methods. Our approach
has broad applicability and can be used in diverse change-point models.
