# Sequential change detection via backward confidence sequences

arXiv: https://arxiv.org/abs/2302.02544 · HTML: https://mlsanity.com/paper/2302.02544/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Tracking the risk of a deployed model and detecting harmful distribution shifts](https://mlsanity.com/paper/2110.06177/) (2021)
- [Sequential estimation of quantiles with applications to A/B-testing and best-arm identification](https://mlsanity.com/paper/1906.09712/) (2019)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [Catoni-style confidence sequences for heavy-tailed mean estimation](https://mlsanity.com/paper/2202.01250/) (2022)
- [Bregman Deviations of Generic Exponential Families](https://mlsanity.com/paper/2201.07306/) (2022)
- [Change Detection with the Kernel Cumulative Sum Algorithm](https://mlsanity.com/paper/1903.01661/) (2019)
- [Sequential change-point detection based on nearest neighbors](https://mlsanity.com/paper/1604.03611/) (2016)
- [Differentially Private Change-Point Detection](https://mlsanity.com/paper/1808.10056/) (2018)
- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [Huber-Robust Confidence Sequences](https://mlsanity.com/paper/2301.09573/) (2023)
- [Adversarially robust change point detection](https://mlsanity.com/paper/2105.10417/) (2021)

## Built on by (most cited first, 3 of 3)

- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Online Heavy-tailed Change-point detection](https://mlsanity.com/paper/2306.09548/) (2023)

## Abstract (arXiv)

We present a simple reduction from sequential estimation to sequential changepoint detection (SCD). In short, suppose we are interested in detecting changepoints in some parameter or functional θ of the underlying distribution. We demonstrate that if we can construct a confidence sequence (CS) for θ, then we can also successfully perform SCD for θ. This is accomplished by checking if two CSs -- one forwards and the other backwards -- ever fail to intersect. Since the literature on CSs has been rapidly evolving recently, the reduction provided in this paper immediately solves several old and new change detection problems. Further, our "backward CS", constructed by reversing time, is new and potentially of independent interest. We provide strong nonasymptotic guarantees on the frequency of false alarms and detection delay, and demonstrate numerical effectiveness on several problems.