Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection
Abstract
Generalized stochastic approximation replaces the log-likelihood ratio of a sequential change-point problem by an affine function of a fixed feature dictionary, whose coefficients solve a normal system in the dictionary's moments under the pre- and post-change laws. The increment is a rescaled orthogonal projection of the bounded score, and the information it carries is bounded by the triangular discrimination between the laws. The dictionary decides what is detectable: a symmetry shared by both laws annihilates a whole parity at every order, and one further column raises the information by an explicit bordered-metric increment. A single efficiency factor, at most one, governs all three procedures the increment drives -- cumulative-sum, Shiryaev-Roberts and Shiryaev -- through false-alarm and delay bounds valid at every threshold. Estimated coefficients are consistent and asymptotically normal. A Monte-Carlo study measures the factor against the delay ratio it predicts, and locates the order at which the dictionary stops paying.
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BibTeX
@misc{zabolotnii2026generalized,
title = {{Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection}},
author = {Serhii Zabolotnii},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.23419},
eprint = {2605.23419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.23419},
}
RIS
TY - UNPB
TI - Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection
AU - Serhii Zabolotnii
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2605.23419
UR - https://arxiv.org/abs/2605.23419
AB - Generalized stochastic approximation replaces the log-likelihood ratio of a sequential change-point problem by an affine function of a fixed feature dictionary, whose coefficients solve a normal system in the dictionary's moments under the pre- and post-change laws. The increment is a rescaled orthogonal projection of the bounded score, and the information it carries is bounded by the triangular discrimination between the laws. The dictionary decides what is detectable: a symmetry shared by both laws annihilates a whole parity at every order, and one further column raises the information by an explicit bordered-metric increment. A single efficiency factor, at most one, governs all three procedures the increment drives -- cumulative-sum, Shiryaev-Roberts and Shiryaev -- through false-alarm and delay bounds valid at every threshold. Estimated coefficients are consistent and asymptotically normal. A Monte-Carlo study measures the factor against the delay ratio it predicts, and locates the order at which the dictionary stops paying.
ER -