# Sequential Gradient Descent and Quasi-Newton's Method for Change-Point Analysis

arXiv: https://arxiv.org/abs/2210.12235 · HTML: https://mlsanity.com/paper/2210.12235/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [SGD without Replacement: Sharper Rates for General Smooth Convex Functions](https://mlsanity.com/paper/1903.01463/) (2019)
- [Closing the convergence gap of SGD without replacement](https://mlsanity.com/paper/2002.10400/) (2020)
- [Multiple Change-point Detection: a Selective Overview](https://mlsanity.com/paper/1512.04093/) (2015)
- [Structural Breaks in Time Series](https://mlsanity.com/paper/1805.03807/) (2018)

## Built on by (most cited first, 2 of 2)

- [Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2410.20670/) (2024)
- [Adaptive Testing for Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2511.06645/) (2025)

## Abstract (arXiv)

One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. This paper introduces a new sequential method (SE) that can be coupled with gradient descent (SeGD) and quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.