Ms.FPOP: An Exact and Fast Segmentation Algorithm With a Multiscale Penalty

Given a time series in $R^n$ with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm to minimize a least square criterion with a multiscale penalty promoting well-spread changepoints. Such a penalty has been proposed in Verzelen et al. (2020), and it achieves optimal rates for changepoint detection and changepoint localization. Our proposed algorithm, named Ms.FPOP, extends functional pruning ideas of Rigaill (2015) and Maidstone et al. (2017) to multiscale penalties. For large signals, $n \geq 10^5$, with relatively few real changepoints, Ms.FPOP is typically quasi-linear and an order of magnitude faster than PELT. We propose an efficient C++ implementation interfaced with R of Ms.FPOP allowing to segment a profile of up to $n = 10^6$ in a matter of seconds. Finally, we illustrate on simple simulations that for large enough profiles ($n \geq 10^4$) Ms.FPOP using the multiscale penalty of Verzelen et al. (2020) is typically more powerfull than FPOP using the classical BIC penalty of Yao (1989).