Seeded intervals and noise level estimation in change point detection: a discussion of Fryzlewicz (2020)
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DISCUSSION
Seeded intervals and noise level estimation in change point detection: a discussion of Fryzlewicz (2020) Solt Kovács1 · Housen Li2 · Peter Bühlmann1 Received: 9 June 2020 / Accepted: 12 June 2020 © Korean Statistical Society 2020
Abstract In this discussion, we compare the choice of seeded intervals and that of random intervals for change point segmentation from practical, statistical and computational perspectives. Furthermore, we investigate a novel estimator of the noise level, which improves many existing model selection procedures (including the steepest drop to low levels), particularly for challenging frequent change point scenarios with low signal-to-noise ratios. Keywords Break points · Fast computation · Model selection · Reproducibility · Seeded binary segmentation · Steepest drop to low levels · Variance estimation · Wild binary segmentation 2
1 Starting remarks We congratulate Piotr Fryzlewicz for his interesting and stimulating paper entitled “Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection” (see Fryzlewicz 2020) and we also thank the Editor of the Journal of the Korean Statistical Society for the invitation to write a discussion! We also take the opportunity to express that we have been very much inspired by Fryzlewicz’ previous work on change point detection. We mention in particular his pathbreaking work on wild binary segmentation (Fryzlewicz 2014) which has heavily shaped the thinking on change point detection as well as the narrowest over threshold method (Baranowski et al. 2019). Our remarks and comments should be seen in this light, owing credit to many pioneering ideas from Fryzlewicz. His current paper proposes a new change point detection algorithm (WBS2) that might be thought of as a This comment refers to the article https://doi.org/10.1007/s42952-020-00060-x. * Solt Kovács [email protected] 1
Seminar for Statistics, ETH Zurich, Zurich, Switzerland
2
Institute for Mathematical Stochastics, University of Göttingen, Göttingen, Germany
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hybrid between binary segmentation (BS, Vostrikova 1981) and wild binary segmentation (WBS, Fryzlewicz 2014), as well as a novel model selection procedure (steepest drop to low levels, SDLL). While recently several algorithms have been proposed for change point detection, some of which are computationally very efficient, less attention is paid to model selection which in our point of view remains a difficult task. We thus welcome and appreciate new methods such as SDLL that contribute to model selection. In the following we would like to point to a number of alternatives and modifications that might lead to improved performance in terms of stability/reproducibility, estimation error, range of extendability and computational speed.
2 A summary of seeded binary segmentation (SeedBS, Kovács et al. 2020a) The computational cost for evaluating the CUSUM stat
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