Narrowest-Over-Threshold Detection of Multiple Change Points and Change-Point-Like Features

Abstract

Summary We propose a new, generic and flexible methodology for non‐parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest‐over‐threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.

Univariate mean change point detection: Penalization, CUSUM and optimality

“…In the last few years, a considerable amount of efforts have been made into developing variants of BS in order to handle multiple change points scenarios, see e.g. Fryzlewicz (2014), Baranowski et al (2016) and Eichinger and Kirch (2018).…”

Bayesian Detection of Piecewise Linear Trends in Replicated Time-Series with Application to Growth Data Modelling

“…All three samplers were applied using the following set of hyper-parameter values: α 0 = 0.1, β 0 = 0.1, ν 0 = 0.005. The prior distribution on the number of change-points Figure 2: Benchmarking the estimation of the number of change-points arising from the narrowest-over-threshold ("not") method of Baranowski et al (2016) and our MCMC sampler with fixed different variance (s1), fixed shared variance (s2) and unknown different variance (s3) per time-series, under the complexity prior distribution. The number after the name of each sampler indicates the true number of change-points and for each value 100 synthetic datasets were simulated.…”

“…Our results are benchmarked against the not package available in the Comprehensive R Archive Network, which implements the narrowest-over-threshold method of Baranowski et al (2016). The number of change-points is inferred using a strengthened version of the Bayesian Information Criterion (Liu et al, 1997;Fryzlewicz et al, 2014).…”

“…There are relatively few studies looking specifically at a change-in-slope model (Schroeder and Fryzlewicz, 2013;Cahill et al, 2015;Baranowski et al, 2016;Fearnhead et al, 2018), although they only consider a single time-series. Popular non-Bayesian methods such as binary segmentation (Scott and Knott, 1974;Fryzlewicz et al, 2014) do not work for detecting changes-in-slope (Baranowski et al, 2016). Furthermore, standard dynamic programming approaches (Jackson et al, 2005;Killick et al, 2012) cannot be directly applied to our problem as discussed by Fearnhead et al (2018).…”

Pruning and Nonparametric Multiple Change Point Detection

“…For instance, additional knowledge about the data, such as the type of changes which are to be detected, or computational time considerations might direct a user to particular goodness-of-fit metrics. This plug-and-play idea is similar to that in [4], such that the users can specify their own goodness-of-fit metrics, or pick from available options based on performance with training data. The cp3o procedure makes use of dynamic programming with search space pruning.…”