Kernel Change-Point Detection under Dependence for Unsupervised Text Segmentation

Unsupervised text segmentation is important because boundary labels are expensive, subjective, and often fail to transfer across domains or granularity choices. Text segmentation can be viewed as detecting distributional changes in sequences of pretrained representations, yet existing kernel change-point detection (KCPD) theory largely assumes independent observations. To provide a principled analysis beyond the usual i.i.d. setting, we study penalized KCPD under $m$-dependence, a stylized finite-memory model of short-range dependence, and establish an oracle inequality for the population penalized risk together with a conservative localization guarantee. Building on this perspective, we introduce Embed-KCPD, a training-free method that represents text units with pretrained sentence embeddings and estimates boundaries using penalized KCPD. To complement the theory empirically, we introduce an LLM-based simulation framework that generates synthetic documents with known boundaries and controlled short-range dependence. Across standard text segmentation benchmarks, Embed-KCPD is competitive with and often outperforms strong unsupervised baselines. We further show that its segments are useful beyond intrinsic boundary-based evaluation, serving as effective chunks for evidence retrieval in retrieval-augmented generation (RAG) systems.