Quickest Change-point Detection in Generalized Linear Models with Variational Estimation
Abstract
We consider quickest change-point detection in generalized linear models when the post-change parameter is unknown. Such problems arise, for example, when monitoring whether the relationship between a learned representation and an observed response changes over time. Since detection must occur soon after a change, the post-change parameter must be estimated from a limited number of observations, making finite-sample estimation accuracy particularly important. We propose a window-limited CUSUM procedure that estimates the post-change parameter using a variational-inequality (VI) formulation. For noncanonical links, VI estimation can offer favorable finite-sample accuracy over short windows despite the asymptotic efficiency advantage of maximum likelihood estimation. We characterize how estimation error reduces the effective post-change information rate and affects detection delay, and derive finite-window guarantees accounting for both statistical error and incomplete numerical optimization. The resulting procedure retains false-alarm control and achieves first-order asymptotic optimality under suitable conditions. Numerical experiments compare detection delay and update cost for fixed-budget estimation and benchmark VI-WLCUSUM against alternative detectors.
Related
- Robust Quickest Change Detection with Cost-Efficient Experiment Design and Unknown Post-Change Model
- A Mixture-of-Experts Framework for Multi-Stream Quickest Change Detection
- Quickest Change Detection with Diffusion-Integrated Scores
- Pollak's Minimax Quickest Change Detection: Non-Asymptotic Optimality
- Online Change-Point Detection in Linear Regression with Autoregressive Errors via Streaming Variational Bayes
BibTeX
@misc{lee2026quickest,
title = {{Quickest Change-point Detection in Generalized Linear Models with Variational Estimation}},
author = {Jonghyeok Lee and Yao Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16616},
eprint = {2610.16616},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16616},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quickest Change-point Detection in Generalized Linear Models with Variational Estimation
AU - Jonghyeok Lee
AU - Yao Xie
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16616
UR - https://arxiv.org/abs/2610.16616
AB - We consider quickest change-point detection in generalized linear models when the post-change parameter is unknown. Such problems arise, for example, when monitoring whether the relationship between a learned representation and an observed response changes over time. Since detection must occur soon after a change, the post-change parameter must be estimated from a limited number of observations, making finite-sample estimation accuracy particularly important. We propose a window-limited CUSUM procedure that estimates the post-change parameter using a variational-inequality (VI) formulation. For noncanonical links, VI estimation can offer favorable finite-sample accuracy over short windows despite the asymptotic efficiency advantage of maximum likelihood estimation. We characterize how estimation error reduces the effective post-change information rate and affects detection delay, and derive finite-window guarantees accounting for both statistical error and incomplete numerical optimization. The resulting procedure retains false-alarm control and achieves first-order asymptotic optimality under suitable conditions. Numerical experiments compare detection delay and update cost for fixed-budget estimation and benchmark VI-WLCUSUM against alternative detectors.
ER -