ARM: Detector-Agnostic Changepoint Attribution with Finite-Sample Error Control
2026-08-03 • Artificial Intelligence
Artificial IntelligenceComputer Vision and Pattern Recognition
AI summaryⓘ
The authors introduce ARM, a method that not only detects when a change happens in multiple data streams but also identifies which specific parts changed and how. Unlike previous methods, ARM works reliably even if the exact change point isn’t known precisely, and it controls for errors when making these identifications. They show theoretically and through simulations that ARM keeps error rates low, even with many variables and complex dependencies. When applied to financial data from 2008, ARM correctly identified changes in all major asset classes and ignored control data, demonstrating practical effectiveness.
changepoint detectionmultivariate time serieserror controlfamily-wise error ratefalse discovery ratepermutation testsrank statisticshigh-dimensional data
Authors
Chenchen Peng, Mixia Wu, Qijing Yan, Da Chen, Zhiqi Shen
Abstract
Detecting a change in a multivariate series answers only the first of two questions; the operational question is which coordinates changed. Existing answers are incomplete. Block-level procedures certify predefined groups of coordinates under an additive union bound, high-dimensional variable-selection methods return interpretable rankings without error guarantees, and the post-detection inference literature controls error along the time axis rather than across coordinates. We propose ARM (Attribution by Rank Maxima), a wrapper that accepts a changepoint located by an arbitrary detector and returns the set of coordinates certified to have changed, each carrying a location or scale type label. ARM scores each coordinate by a max-over-splits rank statistic. Because this statistic dominates the corresponding statistic at the estimated split, the resulting certificate is invariant to the manner, and to the accuracy, of the changepoint estimate. Three finite-sample guarantees follow from within-coordinate ranks alone: per-coordinate validity under any detector; exact family-wise error control through a Westfall--Young joint permutation that preserves cross-coordinate dependence, with a fully distribution-free Holm fallback; and false discovery rate control under arbitrary coordinate dependence in high dimensions through Benjamini--Yekutieli and e-BH. In simulations, naive per-coordinate testing at the estimated changepoint inflates its family-wise error beyond $0.66$ as the dimension grows, whereas ARM maintains the nominal level while retaining validity under heavy tails, power in high dimensions, and accurate type labels. On five financial series surrounding the 2008 collapse, ARM attributes a scale change to every asset class and excludes injected control coordinates.