Multiscale Quantile Segmentation

Vanegas, Laura Jula; Behr, Merle; Munk, Axel

doi:10.1080/01621459.2020.1859380

Cited by 12 publications

(10 citation statements)

References 60 publications

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“…To the best of our knowledge, Zou et al (2014) is one of very few examples yielding a procedure for nonparametric change point detection with provable guarantees on localization. A detailed comparison between our results and the ones of Zou et al (2014) will be given in Appendix A, which also includes detailed comparisons of our work with Pein, Sieling and Munk (2017), Vanegas, Behr and Munk (2019) and Garreau and Arlot (2018).…”

Section: Introductionmentioning

confidence: 88%

“…Another interesting contrast can be made between the Kolmogorov-Smirnov detector and the multiscale quantile segmentation method in Vanegas, Behr and Munk (2019). Both algorithms make no assumptions on the distributional form of the cumulative distribution functions.…”

Section: Appendix A: Comparisonsmentioning

confidence: 99%

“…Fearnhead and Rigaill (2018) devised a mean change point detection method which is robust to outliers. Vanegas, Behr and Munk (2019) constructed a multiscale method for detecting changes in a fixed quantile of the distributions. Arlot, Celisse and Harchaoui (2019) considered a kernel version of the cumulative sum (CUSUM) statistic and an 0 -type optimization procedure which can be solved by dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

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Optimal nonparametric change point analysis

Padilla

Wang

et al. 2021

Electron. J. Statist.

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We study change point detection and localization for univariate data in fully nonparametric settings, in which at each time point, we acquire an independent and identically distributed sample from an unknown distribution that is piecewise constant. The magnitude of the distributional changes at the change points is quantified using the Kolmogorov-Smirnov distance. Our framework allows all the relevant parameters, namely the minimal spacing between two consecutive change points, the minimal magnitude of the changes in the Kolmogorov-Smirnov distance, and the number of sample points collected at each time point, to change with the length of the time series. We propose a novel change point detection algorithm based on the Kolmogorov-Smirnov statistic and show that it is nearly minimax rate optimal. Our theory demonstrates a phase transition in the space of model parameters. The phase transition separates parameter combinations for which consistent localization is possible from the ones for which this task is statistically infeasible. We provide extensive numerical experiments to support our theory.

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Section: Introductionmentioning

confidence: 88%

Section: Appendix A: Comparisonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal nonparametric change point analysis

Padilla

Wang

et al. 2021

Electron. J. Statist.

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“…Next, we estimate K clusters from the obtained error scores. Multiscale quantile segmentation (MQS) is a way to partition the error scores into K clusters at K − 1 quantiles [15]. Here, we adopted MQS, denoted by J , to presumably identify pseudo error labels c i ∈ {1, • • • , K} mapped from e i , i.e.…”

Section: Self-supervised Mixture Of Expertsmentioning

confidence: 99%

Generalised Super Resolution for Quantitative MRI Using Self-supervised Mixture of Experts

Lin

Zhou

Slator

et al. 2021

Medical Image Computing and Computer Assisted Intervention – MICCAI 2021

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Multi-modal and multi-contrast imaging datasets have diverse voxel-wise intensities. For example, quantitative MRI acquisition protocols are designed specifically to yield multiple images with widelyvarying contrast that inform models relating MR signals to tissue characteristics. The large variance across images in such data prevents the use of standard normalisation techniques, making super resolution highly challenging. We propose a novel self-supervised mixture-of-experts (SS-MoE) paradigm for deep neural networks, and hence present a method enabling improved super resolution of data where image intensities are diverse and have large variance. Unlike the conventional MoE that automatically aggregates expert results for each input, we explicitly assign an input to the corresponding expert based on the predictive pseudo error labels in a self-supervised fashion. A new gater module is trained to discriminate the error levels of inputs estimated by Multiscale Quantile Segmentation. We show that our new paradigm reduces the error and improves the robustness when super resolving combined diffusion-relaxometry MRI data from the Super MUDI dataset. Our approach is suitable for a wide range of quantitative MRI techniques, and multi-contrast or multi-modal imaging techniques in general. It could be applied to super resolve images with inadequate resolution, or reduce the scanning time needed to acquire images of the required resolution. The source code and the trained models are available at https://github.com/hongxiangharry/SS-MoE.

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“…Several efforts in this direction have been recently made for univariate data. Pein et al (2017) proposed a version of the SMUCE algorithm (Frick et al, 2014) that is sensitive to mean changes, but robust to changes in variance; Zou et al (2014) introduced a nonparametric estimator that can detect general distributions shifts; as an extension of Zou et al (2014), Haynes et al (2017) simplified the loss function in Zou et al (2014) and adopted the pruned exact linear time algorithm (Killick et al, 2012) to improve the computational efficiency; Padilla et al (2018) considered a nonparametric procedure for sequential change point detection; Fearnhead and Rigaill (2018) focused on univariate mean change point detection constructing an estimator that is robust to outliers; Jula Vanegas et al (2021) proposed an estimator for detecting changes in pre-specified quantiles of the generative model; and Padilla et al (2019) developed a nonparametric version of binary segmentation (e.g. Scott and Knott, 1974) based on the Kolmogorov-Smirnov statistic.…”

Section: Introductionmentioning

confidence: 99%