Computationally Efficient Changepoint Detection for a Range of Penalties

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. Recent work in the penalised optimisation setting has focussed on developing an exact pruning-based approach which, 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. To this end we present a method that enables us to find the solution path for all choice of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable 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.

A computationally efficient nonparametric approach for changepoint detection

“…We overcome this problem by using CROPS (Haynes et al 2016), which detects the changepoints for multiple penalty values over a continuous range. Future research could look at an alternative pruning method, cp3o, proposed by James and Matteson (2015) which used probabilistic pruning.…”

“…As before, to implement NMCD we used the nmcdr R package (Zou and Zhange 2014) which is written in FORTRAN with an R user interface. We use the changepoint.np R package (Haynes 2016) to run ED-PELT which also has an R interface but with the main body of the code written in C. We use the default parameters for nmcd and for ED-PELT we use the SIC/BIC penalty term, 2 p log(n), where p is the number of parameters, to match the penalty term used in the nmcd algorithm.…”

“…There are also advantages to being able to compare segmentations with different number of changepoints. Haynes et al (2016) propose a method, Changepoints over a Range Of PenaltieS (CROPS), which efficiently finds all the optimal segmentations for penalty values across a continuous range. This involves an iterative procedure which chooses values of ξ n to run ED-PELT on, based on the segmentations obtained from previous runs of ED-PELT for different penalty values.…”

“…The quality of the final segmentation can be sensitive to this choice, and whilst there are default choices these do not always work well. However we show that the Changepoints for a Range of PenaltieS (CROPS) algorithm (Haynes et al 2016) can be used with ED-PELT to explore optimal segmentations for a range of penalties.…”

“…PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints. To overcome this issue we use a relatively new method, changepoints over a range of penalties (Haynes et al 2016), which finds all of the optimal segmentations for multiple penalty values over a continuous range. We apply our method to detect changes in heart-rate during physical activity.…”