Optimal Detection of Changepoints With a Linear Computational Cost

Abstract

We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.

A computationally efficient nonparametric approach for changepoint detection

“…This involves firstly an alternative numerical approximation to the integral (2.3), which is more efficient to calculate. In addition we use a more efficient dynamic programming algorithm, PELT (Killick et al 2012), to then minimise the cost function.…”

“…To speed up computation, resorted to a screening procedure which means that the estimated segmentation is no longer guaranteed to be the global minimum of the cost function. We show that the screening procedure adversely affects the accuracy of the changepoint detection method, and show how a faster dynamic programming algorithm, pruned exact linear time (PELT) (Killick et al 2012), can be used to find the optimal segmentation with a computational cost that can be close to linear in the amount of data. PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints.…”

“…For example a common approach is to introduce a model for the data within a segment, use minus the maximum of the resulting log-likelihood to define a cost for a segment, and then define a cost of a segmentation as the sum of the costs for each of its segments. See for example Yao (1988), Lavielle (2005), Killick et al (2012) and Davis et al (2006). Finally, the segmentation of the data is obtained as the one that minimises a penalised version of this cost (see also Frick et al 2014, for an extension of these approaches).…”

“…Our method firstly involves simplifying the definition of the segment cost, so that calculating the cost for a given segment involves computation that is O(log n) rather than O(n). Secondly we apply a different dynamic programming approach, pruned exact linear time (PELT) (Killick et al 2012), that is substantially quicker than Segment Neighbourhood Search; for many situations where the number of changepoints increases linearly with n, PELT has been proven to have a computational cost that is linear in n.…”

Using Sensors to Study Home Activities

“…A manual setting is used for the penalty function so that the number of change points can be adjusted. The change points detection algorithm is the pruned exact linear time (PELT) [57] which is computationally efficient and provides an exact segmentation. By applying the change points detection algorithm upon the re-sampled data, we obtain a sequence of 1s and 0s, where "1" represents the presence of a change point and "0" as absence.…”