Restarted Bayesian Online Change-point Detector achieves Optimal Detection Delay
Reda Alami, Odalric Maillard, Raphael Feraud
Abstract
we consider the problem of sequential change-point detection where both the change-points and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory, we derive a variant of the Bayesian Online Change Point Detector proposed by \cite{fearnhead2007line} which is easier to analyze than the original version while keeping its powerful message-passing algorithm. We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and real-world data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy.
BibTeX
@InProceedings{pmlr-v119-alami20a,
title = {Restarted {B}ayesian Online Change-point Detector achieves Optimal Detection Delay},
author = {Alami, Reda and Maillard, Odalric and Feraud, Raphael},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {211--221},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/alami20a/alami20a.pdf},
url = {https://proceedings.mlr.press/v119/alami20a.html},
abstract = {we consider the problem of sequential change-point detection where both the change-points and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory, we derive a variant of the Bayesian Online Change Point Detector proposed by \cite{fearnhead2007line} which is easier to analyze than the original version while keeping its powerful message-passing algorithm. We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and real-world data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy.}
}