# On Optimal Multiple Changepoint Algorithms for Large Data

arXiv: https://arxiv.org/abs/1409.1842 · HTML: https://mlsanity.com/paper/1409.1842/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2014.

## Built on by (most cited first, 15 of 15)

- [Fast Online Changepoint Detection via Functional Pruning CUSUM statistics](https://mlsanity.com/paper/2110.08205/) (2021)
- [Causal Discovery-Driven Change Point Detection in Time Series](https://mlsanity.com/paper/2407.07290/) (2024)
- [Penalty Learning for Optimal Partitioning using Multilayer Perceptron](https://mlsanity.com/paper/2408.00856/) (2024)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data](https://mlsanity.com/paper/2106.11541/) (2021)
- [Optimizing ROC Curves with a Sort-Based Surrogate Loss Function for Binary Classification and Changepoint Detection](https://mlsanity.com/paper/2107.01285/) (2021)
- [Mixture of segmentation for heterogeneous functional data](https://mlsanity.com/paper/2303.10712/) (2023)
- [Functional Labeled Optimal Partitioning](https://mlsanity.com/paper/2210.02580/) (2022)
- [The DeepCAR Method: Forecasting Time-Series Data That Have Change Points](https://mlsanity.com/paper/2302.11241/) (2023)
- [Geometric-Based Pruning Rules For Change Point Detection in Multiple Independent Time Series](https://mlsanity.com/paper/2306.09555/) (2023)
- [Efficient line search for optimizing Area Under the ROC Curve in gradient descent](https://mlsanity.com/paper/2410.08635/) (2024)
- [Finite Sample Complexity Analysis of Binary Segmentation](https://mlsanity.com/paper/2410.08654/) (2024)
- [Learning Penalty for Optimal Partitioning via Automatic Feature Extraction](https://mlsanity.com/paper/2505.07413/) (2025)
- [skchange: Fast and Flexible Algorithms for Changepoint Detection](https://mlsanity.com/paper/2608.19767/) (2026)
- [Distribution-free inference on the number of changepoints](https://mlsanity.com/paper/2609.08234/) (2026)

## Abstract (arXiv)

There is an increasing need for algorithms that can accurately detect changepoints in long time-series, or equivalent, data. Many common approaches to detecting changepoints, for example based on penalised likelihood or minimum description length, can be formulated in terms of minimising a cost over segmentations. Dynamic programming methods exist to solve this minimisation problem exactly, but these tend to scale at least quadratically in the length of the time-series. Algorithms, such as Binary Segmentation, exist that have a computational cost that is close to linear in the length of the time-series, but these are not guaranteed to find the optimal segmentation. Recently pruning ideas have been suggested that can speed up the dynamic programming algorithms, whilst still being guaranteed to find true minimum of the cost function. Here we extend these pruning methods, and introduce two new algorithms for segmenting data, FPOP and SNIP. Empirical results show that FPOP is substantially faster than existing dynamic programming methods, and unlike the existing methods its computational efficiency is robust to the number of changepoints in the data. We evaluate the method at detecting Copy Number Variations and observe that FPOP has a computational cost that is competitive with that of Binary Segmentation.