An Optimal False Discovery Rate Controlling Procedure for Changepoint Detection

2026/07/31 by Louis Davis, Guenther Walther
Mathematics · #stat.ME

paper · pdf

46 pages, 3 figures

arxiv created 2026/07/31 · arxiv updated 2026/08/04

Abstract

We consider the problem of detecting and localizing a growing number of changepoints in a sequence of independent observations. We propose a new method, Lean Bonferroni Detection - False Discovery Rate (LBD-FDR), which produces a set of localized regions in the data sequence where, in expectation, a high proportion of them contain a changepoint. LBD-FDR guarantees control of the false discovery rate in a wide range of distributional settings, including the challenging case of independent non-parametric and heavy-tailed data. For independent Gaussian sequences, we derive conditions on changepoint arrangements where the method consistently detects all changepoints with a large enough signal while simultaneously being unaffected by those that are undetectable, and we show that LBD-FDR obtains the optimal detection constant in certain regimes. Moreover, we derive the settings where our method is more powerful than the minimax optimal Type I error controlling method. We finally develop a computationally feasible algorithm for the LBD-FDR and compare it in simulation to five existing procedures.

Citations

• Controlling the false discovery rate under a non-parametric graphical dependence model
• Diversifying Conformal Selections
• Bringing closure to FDR control: beating the e-Benjamini-Hochberg procedure
• Fast and Optimal Changepoint Detection and Localization using Bonferroni Triplets
• Multiscale Quantile Regression with Local Error Control
• Tail bounds for empirically standardized sums
• Robust Narrowest Significance Pursuit: Inference for multiple change-points in the median
• Optimal Change-Point Detection and Localization
• Narrowest Significance Pursuit: inference for multiple change-points in linear models
• Conditional calibration for false discovery rate control under dependence
• Large-scale inference with block structure
• Multiscale quantile segmentation
• Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection
• Filtering the rejection set while preserving false discovery rate\n control
• On spike and slab empirical Bayes multiple testing
• Structural Breaks in Time Series
• Optimal Rates and Tradeoffs in Multiple Testing
• Changepoint Detection in the Presence of Outliers
• Distribution-free Multiple Testing
• Multiple Change-point Detection: a Selective Overview
• Multiple Change-Point Detection: A Selective Overview
• Heterogeneous Change Point Inference
• Multiscale Change-Point Inference
• Adapting to Unknown Sparsity by controlling the False Discovery Rate
• Adapting to unknown sparsity by controlling the false discovery rate
• The control of the false discovery rate in multiple testing under dependency
• On cliques in graphs
• CONTINUOUS INSPECTION SCHEMES