Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss Article Swipe

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Cesare Alippi , Giacomo Boracchi , Diego Carrera , Manuel Roveri ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1510.04850

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 \emph{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).

Related Topics

Gaussian Function

Multivariate Normal Distribution

Mathematics

Statistics

Computer Science

Artificial Intelligence

Concepts

Dimension (graph theory) Divergence (linguistics) Change detection Gaussian Variance (accounting) Multivariate statistics Multivariate normal distribution Kullback–Leibler divergence Mathematics Magnitude (astronomy) Statistics Computer science Artificial intelligence Physics Combinatorics Linguistics Quantum mechanics Philosophy Accounting Business Astronomy

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1510.04850
PDF: https://arxiv.org/pdf/1510.04850
OA Status: green
Cited By: 4
References: 23
Related Works: 20
OpenAlex ID: https://openalex.org/W2201315292

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DOI: https://doi.org/10.48550/arxiv.1510.04850

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Title: Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss

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Type: preprint

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Language: en

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Publication year: 2015

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Publication date: 2015-10-16

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Authors: Cesare Alippi, Giacomo Boracchi, Diego Carrera, Manuel Roveri

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Landing page: https://arxiv.org/abs/1510.04850

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Concepts: Dimension (graph theory), Divergence (linguistics), Change detection, Gaussian, Variance (accounting), Multivariate statistics, Multivariate normal distribution, Kullback–Leibler divergence, Mathematics, Magnitude (astronomy), Statistics, Computer science, Artificial intelligence, Physics, Combinatorics, Linguistics, Quantum mechanics, Philosophy, Accounting, Business, Astronomy

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Cited by: 4

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Citations by year (recent): 2024: 1, 2021: 1, 2020: 2

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References (count): 23

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Related works (count): 20

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