# Heterogeneous Change Point Inference

arXiv: https://arxiv.org/abs/1505.04898 · HTML: https://mlsanity.com/paper/1505.04898/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2015.

## Built on by (most cited first, 4 of 4)

- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [SoccerCPD: Formation and Role Change-Point Detection in Soccer Matches Using Spatiotemporal Tracking Data](https://mlsanity.com/paper/2206.10926/) (2022)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Score-based change point detection via tracking the best of infinitely many experts](https://mlsanity.com/paper/2408.14073/) (2024)

## Abstract (arXiv)

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.