# Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection

arXiv: https://arxiv.org/abs/2605.23419 · HTML: https://mlsanity.com/paper/2605.23419/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2026.

## Built on by (most cited first, 1 of 1)

- [Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis](https://mlsanity.com/paper/2607.06089/) (2026)

## Abstract (arXiv)

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.