Electronic Journal of Statistics

Change detection via affine and quadratic detectors

Yang Cao, Arkadi Nemirovski, Yao Xie, Vincent Guigues, and Anatoli Juditsky

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The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, “Hypothesis testing via affine detectors,” Electronic Journal of Statistics 10:2204–2242, 2016. Namely, we consider the Change Detection problem as follows: observing one by one noisy observations of outputs of a discrete-time linear dynamical system, we intend to decide, in a sequential fashion, on the null hypothesis that the input to the system is a nuisance, vs. the alternative that the input is a “nontrivial signal,” with both the nuisances and the nontrivial signals modeled as inputs belonging to finite unions of some given convex sets. Assuming the observation noises are zero mean sub-Gaussian, we develop “computation-friendly” sequential decision rules and demonstrate that in our context these rules are provably near-optimal.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 1-57.

Received: February 2017
First available in Project Euclid: 3 January 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C20: Minimax procedures
Secondary: 90C22: Semidefinite programming

Change-point detection semi-definite program

Creative Commons Attribution 4.0 International License.


Cao, Yang; Nemirovski, Arkadi; Xie, Yao; Guigues, Vincent; Juditsky, Anatoli. Change detection via affine and quadratic detectors. Electron. J. Statist. 12 (2018), no. 1, 1--57. doi:10.1214/17-EJS1373. https://projecteuclid.org/euclid.ejs/1514970025

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