# Multiscale Change-Point Inference

arXiv: https://arxiv.org/abs/1301.7212 · HTML: https://mlsanity.com/paper/1301.7212/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2013.

## Built on by (most cited first, 13 of 13)

- [Random Forests for Change Point Detection](https://mlsanity.com/paper/2205.04997/) (2022)
- [Theoretical guarantees for change localization using conformal p-values](https://mlsanity.com/paper/2510.08749/) (2025)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees](https://mlsanity.com/paper/2311.18769/) (2023)
- [Distribution-free root cause analysis](https://mlsanity.com/paper/2605.21627/) (2026)
- [Inference for Change Points in High Dimensional Mean Shift Models](https://mlsanity.com/paper/2107.09150/) (2021)
- [Population based change-point detection for the identification of homozygosity islands](https://mlsanity.com/paper/2111.10187/) (2021)
- [Disentangled Causal Graph Learning for Online Unsupervised Root Cause Analysis](https://mlsanity.com/paper/2305.10638/) (2023)
- [Online Heavy-tailed Change-point detection](https://mlsanity.com/paper/2306.09548/) (2023)
- [Geometric-Based Pruning Rules For Change Point Detection in Multiple Independent Time Series](https://mlsanity.com/paper/2306.09555/) (2023)
- [On Non-Stationary Dynamic Pricing: Adaptivity and Optimality](https://mlsanity.com/paper/2607.24115/) (2026)
- [ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency](https://mlsanity.com/paper/2608.08424/) (2026)

## Abstract (arXiv)

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 α. 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, α 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.