FDR-Control in Multiscale Change-point Segmentation

TL;DR

FDRSeg is a multiscale change-point detection method that controls the false discovery rate, providing accurate segmentation with theoretical guarantees and efficient computation, suitable for large datasets.

Contribution

It introduces FDRSeg, a novel change-point detection method that controls FDR linearly, with proven non-asymptotic bounds, optimal convergence rates, and efficient linear-time algorithms.

Findings

FDRSeg controls FDR linearly with the number of false jumps.

Estimates change-points and signals at near-minimax optimal rates.

Performs well compared to state-of-the-art methods on simulated and real data.

Abstract

Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Change-point locations, as well as the signal, are shown to be estimated in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. $L^p$-risk, $p \ge 1$, over classes of step functions with bounded jump sizes and either bounded, or possibly increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online.