Consistent Kernel Change-Point Detection under m-Dependence for Text Segmentation
This provides improved theoretical and practical reliability for text segmentation tasks, addressing dependencies in real-world sequential data like text.
The paper tackles the problem of kernel change-point detection for text segmentation under data dependencies, proving consistency guarantees for m-dependent data and demonstrating through empirical studies that KCPD with text embeddings outperforms baselines across diverse datasets.
Kernel change-point detection (KCPD) has become a widely used tool for identifying structural changes in complex data. While existing theory establishes consistency under independence assumptions, real-world sequential data such as text exhibits strong dependencies. We establish new guarantees for KCPD under $m$-dependent data: specifically, we prove consistency in the number of detected change points and weak consistency in their locations under mild additional assumptions. We perform an LLM-based simulation that generates synthetic $m$-dependent text to validate the asymptotics. To complement these results, we present the first comprehensive empirical study of KCPD for text segmentation with modern embeddings. Across diverse text datasets, KCPD with text embeddings outperforms baselines in standard text segmentation metrics. We demonstrate through a case study on Taylor Swift's tweets that KCPD not only provides strong theoretical and simulated reliability but also practical effectiveness for text segmentation tasks.