TY - GEN

T1 - CuSum for sequential change diagnosis

AU - Warner, Austin

AU - Fellouris, Georgios

N1 - Funding Information:
This research was supported by the US National Science Foundation under grant AMPS 1736454 through the University of Illinois at Urbana-Champaign.
Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - The problem of sequential change diagnosis is considered, where a sequence of independent random elements is accessed sequentially, there is an abrupt change in its distribution at some unknown time, and there are two main operational goals: to quickly detect the change and to accurately identify the post-change distribution among a finite set of alternatives. A standard algorithm is considered, which does not explicitly address the isolation task and raises an alarm as soon as the CuSum statistic that corresponds to one of the post-change alternatives exceeds a certain threshold. It is shown that in certain cases, such as the so-called multichannel problem, this algorithm controls the worst-case conditional probability of false isolation and minimizes Lorden's criterion, for every possible post-change distribution, to a first-order asymptotic approximation as the false alarm rate goes to zero sufficiently faster than the worst-case conditional probability of false isolation. These theoretical results are also illustrated with a numerical study.

AB - The problem of sequential change diagnosis is considered, where a sequence of independent random elements is accessed sequentially, there is an abrupt change in its distribution at some unknown time, and there are two main operational goals: to quickly detect the change and to accurately identify the post-change distribution among a finite set of alternatives. A standard algorithm is considered, which does not explicitly address the isolation task and raises an alarm as soon as the CuSum statistic that corresponds to one of the post-change alternatives exceeds a certain threshold. It is shown that in certain cases, such as the so-called multichannel problem, this algorithm controls the worst-case conditional probability of false isolation and minimizes Lorden's criterion, for every possible post-change distribution, to a first-order asymptotic approximation as the false alarm rate goes to zero sufficiently faster than the worst-case conditional probability of false isolation. These theoretical results are also illustrated with a numerical study.

KW - Identification

KW - Isolation

KW - Sequential Change Detection

KW - Sequential Change Diagnosis

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U2 - 10.1109/ISIT50566.2022.9834755

DO - 10.1109/ISIT50566.2022.9834755

M3 - Conference contribution

AN - SCOPUS:85136268726

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 486

EP - 491

BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022

Y2 - 26 June 2022 through 1 July 2022

ER -