# Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees

arXiv: https://arxiv.org/abs/2311.18769 · HTML: https://mlsanity.com/paper/2311.18769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 52 references that are in the map.
- First posted on arXiv 30 Nov 2023.

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

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently](https://mlsanity.com/paper/2002.08095/) (2020)
- [Kernel Change-point Detection with Auxiliary Deep Generative Models](https://mlsanity.com/paper/1901.06077/) (2019)
- [Scan B-Statistic for Kernel Change-Point Detection](https://mlsanity.com/paper/1507.01279/) (2015)
- [High-dimensional, multiscale online changepoint detection](https://mlsanity.com/paper/2003.03668/) (2020)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Multiscale Change-Point Inference](https://mlsanity.com/paper/1301.7212/) (2013)
- [Change Detection with the Kernel Cumulative Sum Algorithm](https://mlsanity.com/paper/1903.01661/) (2019)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
- [Sequential Changepoint Detection in Neural Networks with Checkpoints](https://mlsanity.com/paper/2010.03053/) (2020)
- [Confirmatory Bayesian Online Change Point Detection in the Covariance Structure of Gaussian Processes](https://mlsanity.com/paper/1905.13168/) (2019)
- [Multiple Change Point Detection and Validation in Autoregressive Time Series Data](https://mlsanity.com/paper/1912.07775/) (2019)
- [Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching](https://mlsanity.com/paper/2203.09862/) (2022)
- [Learning Linearized Models from Nonlinear Systems with Finite Data](https://mlsanity.com/paper/2309.08805/) (2023)

## Built on by (most cited first, 1 of 1)

- [Guarantees on Dynamical System Distinguishability for LLM Token Generation](https://mlsanity.com/paper/2607.28667/) (2026)

## Abstract (arXiv)

The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.