Efficient penalty search for multiple changepoint problems

TL;DR

This paper introduces a fast, efficient method to compute optimal multiple changepoint segmentations across a continuous range of penalty values, enabling better model selection without heavy computational costs.

Contribution

The authors develop a novel approach that computes changepoint segmentations for all penalties simultaneously, significantly reducing computation time compared to existing methods.

Findings

Computational complexity is linear in data points and penalty range.

Method outperforms traditional approaches in speed, especially with large data.

Enables effective penalty comparison for better segmentation accuracy.

Abstract

In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such methods are typically computationally intensive. Recent work in the penalised optimisation setting has focussed on developing a pruning-based approach which gives an improved computational cost that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. Consequently it is desirable to have an approach that enables us to compare segmentations for different choices of penalty. To this end we present a method to obtain optimal changepoint segmentations of data sequences for all penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitably parsimonious penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. This can be orders of magnitude faster than alternative approaches that find optimal segmentations for a range of the number of changepoints.