Interval Localization for Multiple Change-points with Error Rate Control
Abstract
Interval localization in multiple change-point detection aims to identify intervals containing true change-points while controlling false discoveries. We formulate this task as a multiple testing problem over detector-reported intervals and develop an algorithm-agnostic and distribution-free framework that controls the interval-level FDR, the expected proportion of retained intervals containing no true change-points. The proposed permutation-based order-preserving interval selection (POIS) uses order-preserving sample splitting to separate detection from permutation testing. To improve power, POIS+ reuses the detection-side evidence and introduces detection-conditional e-values as unnormalized weights for permutation p-values. Both procedures achieve finite-sample FDR control. Under the stated conditions, POIS attains asymptotically full power while POIS+ has asymptotically no lower power than POIS. Simulation results show that POIS maintains high power and POIS+ further improves power with empirical FDR below the nominal level for both procedures. Two real data applications demonstrate the practical effectiveness of the proposed methods.
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BibTeX
@misc{wei2026interval,
title = {{Interval Localization for Multiple Change-points with Error Rate Control}},
author = {Zijian Wei and Yajie Bao and Haojie Ren and Nan Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10271},
eprint = {2610.10271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10271},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interval Localization for Multiple Change-points with Error Rate Control
AU - Zijian Wei
AU - Yajie Bao
AU - Haojie Ren
AU - Nan Chen
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10271
UR - https://arxiv.org/abs/2610.10271
AB - Interval localization in multiple change-point detection aims to identify intervals containing true change-points while controlling false discoveries. We formulate this task as a multiple testing problem over detector-reported intervals and develop an algorithm-agnostic and distribution-free framework that controls the interval-level FDR, the expected proportion of retained intervals containing no true change-points. The proposed permutation-based order-preserving interval selection (POIS) uses order-preserving sample splitting to separate detection from permutation testing. To improve power, POIS+ reuses the detection-side evidence and introduces detection-conditional e-values as unnormalized weights for permutation p-values. Both procedures achieve finite-sample FDR control. Under the stated conditions, POIS attains asymptotically full power while POIS+ has asymptotically no lower power than POIS. Simulation results show that POIS maintains high power and POIS+ further improves power with empirical FDR below the nominal level for both procedures. Two real data applications demonstrate the practical effectiveness of the proposed methods.
ER -