Changepoint Detection in Complex Models: Cross-Fitting Is Needed

TL;DR

This paper introduces a cross-fitting approach for changepoint detection that improves accuracy in complex models by reducing overfitting bias, supported by theoretical guarantees and numerical experiments.

Contribution

It proposes a novel out-of-sample loss based cross-fitting method for more reliable changepoint detection in high-dimensional and hyperparameter-tuned models.

Findings

Method significantly improves changepoint detection accuracy.

Theoretical framework guarantees consistency under mild conditions.

Numerical experiments demonstrate enhanced reliability in complex scenarios.

Abstract

Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or hyperparameter tuning -- this strategy can lead to inaccurate changepoint estimation due to over-adaptivity biases. To mitigate this issue, we propose a novel cross-fitting methodology based on out-of-sample loss evaluations, which decouples model fitting from changepoint search. We establish a general theoretical framework for consistent changepoint estimation under mild conditions, and further extend it to temporally dependent data. A key implication of the theory is that consistency depends primarily on the models' predictive accuracy over nearly homogeneous segments. Numerical experiments show that the proposed method substantially improves the reliability and adaptability of changepoint detection in complex scenarios.