{"ID":2847027,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00938","arxiv_id":"2511.00938","title":"Persistence-Based Statistics for Detecting Structural Changes in High-Dimensional Point Clouds","abstract":"We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for classical persistence statistics-total and maximum persistence-under general distributions, with explicit variance-scaling behavior derived for Gaussian mixture models. Building on these results, we introduce a bounded and normalized statistic based on persistence landscapes combined with the Jensen-Shannon divergence, and we prove its Holder continuity with respect to perturbations of the input point clouds. The resulting measure is stable, scale- and shift-invariant, and well suited for finite-sample nonparametric inference via permutation testing. An illustrative numerical study using dynamic attribute vectors from decentralized governance data demonstrates the practical applicability of the proposed method. Overall, this work provides a statistically rigorous and computationally stable approach to change-point detection in complex, high-dimensional data.","short_abstract":"We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for classical persistence statistics-total and maximum persistence-under general dist...","url_abs":"https://arxiv.org/abs/2511.00938","url_pdf":"https://arxiv.org/pdf/2511.00938v2","authors":"[\"Toshiyuki Nakayama\"]","published":"2025-11-02T13:42:44Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.AT\",\"math.PR\"]","methods":"[]","has_code":false}