Heterogeneous Change Point Inference

We propose HSMUCE (heterogeneous simultaneous multiscale change-point estimator) for the detection of multiple change-points of the signal in a heterogeneous gaussian regression model. A piecewise constant function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale dependent critical values in order to keep a global nominal level alpha, even for finite samples. We show that HSMUCE controls the error of over- and underestimation of the number of change-points. To this end, new deviation bounds for F-type statistics are derived. Moreover, we obtain confidence sets for the whole signal. All results are non-asymptotic and uniform over a large class of heterogeneous change-point models. HSMUCE is fast to compute, achieves the optimal detection rate and estimates the number of change-points at almost optimal accuracy for vanishing signals, while still being robust. We compare HSMUCE with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states. An R-package is available online

Multiscale Change-Point Inference

We introduce a new estimator SMUCE (simultaneous multiscale change-point estimator) for the change-point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test at a level \alpha. The probability of overestimating the true number of change-points K is controlled by the asymptotic null distribution of the multiscale test statistic. Further, we derive exponential bounds for the probability of underestimating K. By balancing these quantities, \alpha will be chosen such that the probability of correctly estimating K is maximized. All results are even non-asymptotic for the normal case. Based on the aforementioned bounds, we construct asymptotically honest confidence sets for the unknown step function and its change-points. At the same time, we obtain exponential bounds for estimating the change-point locations which for example yield the minimax rate O(1/n) up to a log term. Finally, SMUCE asymptotically achieves the optimal detection rate of vanishing signals. We illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions. The performance of the proposed multiscale approach is illustrated by simulations and in two cutting-edge applications from genetic engineering and photoemission spectroscopy

Multiscale DNA partitioning: statistical evidence for segments. Bioinformatics

Abstract Motivation: DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as GC content, local ancestry in population genetics, or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria, and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen. Results: Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user specified probability 1−α that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as segmentation method which searches segments of any length (on all scales), simultaneously. It is also very accurate in localizing segments: under bench-mark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Availability: Our method is implemented in function smuceR of the R-package stepR, available fro