# Narrowest-Over-Threshold Detection of Multiple Change-points and Change-point-like Features

arXiv: https://arxiv.org/abs/1609.00293 · HTML: https://mlsanity.com/paper/1609.00293/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2016.

## Built on by (most cited first, 13 of 13)

- [Automatic Change-Point Detection in Time Series via Deep Learning](https://mlsanity.com/paper/2211.03860/) (2022)
- [Segmenting Human-LLM Co-authored Text via Change Point Detection](https://mlsanity.com/paper/2605.03723/) (2026)
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- [An Efficient Continual Learning Framework for Multivariate Time Series Prediction Tasks with Application to Vehicle State Estimation](https://mlsanity.com/paper/2503.01669/) (2025)
- [DMS, AE, DAA: methods and applications of adaptive time series model selection, ensemble, and financial evaluation](https://mlsanity.com/paper/2110.11156/) (2021)
- [Finite Sample Complexity Analysis of Binary Segmentation](https://mlsanity.com/paper/2410.08654/) (2024)
- [Adaptive Testing for Segmenting Watermarked Texts From Language Models](https://mlsanity.com/paper/2511.06645/) (2025)
- [ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency](https://mlsanity.com/paper/2608.08424/) (2026)
- [High-dimensional nonparametric changepoint detection via low-rank degree-two density projection](https://mlsanity.com/paper/2608.13922/) (2026)
- [High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection](https://mlsanity.com/paper/2608.15466/) (2026)
- [skchange: Fast and Flexible Algorithms for Changepoint Detection](https://mlsanity.com/paper/2608.19767/) (2026)
- [A convolutional framework for detecting event-driven dynamics in energy price series](https://mlsanity.com/paper/2609.00402/) (2026)
- [Beyond Sub-Gaussian Detector Scores: Robust Weighted Profile-Loss Change Point Detection for Human-LLM Text Segmentation](https://mlsanity.com/paper/2609.36888/) (2026)

## Abstract (arXiv)

We propose a new, generic and flexible methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function, and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change-points in the piecewise-constant signal model, kinks in the piecewise-linear signal model, and other similar irregularities, which we also refer to as generalised change-points. Our methodology works with only minor modifications across a range of generalised change-point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalised change-point detection device, termed Narrowest-Over-Threshold (NOT). The key ingredient of NOT is its focus on the smallest local sections of the data on which the existence of a feature is suspected. Crucially, this adaptive localisation technique prevents NOT from considering subsamples containing two or more features, a key factor that ensures the general applicability of NOT. For selected scenarios, we show the consistency and near-optimality of NOT in detecting the number and locations of generalised change-points. Furthermore, we propose to select NOT's threshold (automatically) via the strengthened Schwarz Information Criterion (sSIC) and give theoretical justifications. The NOT estimators are easy to implement and rapid to compute: the entire threshold-indexed solution path can be computed in close-to-linear time. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. There is no single competitor, but we show that the performance of NOT matches or surpasses the state of the art in the scenarios tested. Our methodology is implemented in the R package not.