# Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss

arXiv: https://arxiv.org/abs/1510.04850 · HTML: https://mlsanity.com/paper/1510.04850/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2015.

## Built on by (most cited first, 8 of 8)

- [Nonparametric and Online Change Detection in Multivariate Datastreams using QuantTree](https://mlsanity.com/paper/2208.14801/) (2022)
- [Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densities](https://mlsanity.com/paper/2107.05901/) (2021)
- [Pre-treatment of outliers and anomalies in plant data: Methodology and case study of a Vacuum Distillation Unit](https://mlsanity.com/paper/2106.14641/) (2021)
- [Latent Neural Stochastic Differential Equations for Change Point Detection](https://mlsanity.com/paper/2208.10317/) (2022)
- [Deep Open-Set Recognition for Silicon Wafer Production Monitoring](https://mlsanity.com/paper/2208.14071/) (2022)
- [Latent Space Unsupervised Semantic Segmentation](https://mlsanity.com/paper/2207.11067/) (2022)
- [Class Distribution Monitoring for Concept Drift Detection](https://mlsanity.com/paper/2210.08470/) (2022)
- [Change Detection in Multivariate data streams: Online Analysis with Kernel-QuantTree](https://mlsanity.com/paper/2410.13778/) (2024)

## Abstract (arXiv)

We address the problem of detecting changes in multivariate datastreams, and we investigate the intrinsic difficulty that change-detection methods have to face when the data dimension scales. In particular, we consider a general approach where changes are detected by comparing the distribution of the log-likelihood of the datastream over different time windows. Despite the fact that this approach constitutes the frame of several change-detection methods, its effectiveness when data dimension scales has never been investigated, which is indeed the goal of our paper. We show that the magnitude of the change can be naturally measured by the symmetric Kullback-Leibler divergence between the pre- and post-change distributions, and that the detectability of a change of a given magnitude worsens when the data dimension increases. This problem, which we refer to as detectability loss, is due to the linear relationship between the variance of the log-likelihood and the data dimension. We analytically derive the detectability loss on Gaussian-distributed datastreams, and empirically demonstrate that this problem holds also on real-world datasets and that can be harmful even at low data-dimensions (say, 10).