TY - GEN
T1 - Universal sequential outlier hypothesis testing
AU - Li, Yun
AU - Nitinawarat, Sirin
AU - Veeravalli, Venugopal V.
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2015/4/24
Y1 - 2015/4/24
N2 - Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are generated by an 'outlier' distribution, distinct from a common 'typical' distribution governing the majority of the sequences. Apart from being distinct, the outlier and typical distributions can be arbitrarily close. The goal is to design a universal test to best discern all the outlier sequences. A universal test with the flavor of the repeated significance test is proposed and its asymptotic performance is characterized under various universal settings. The proposed test is shown to be universally consistent. For the model with identical outliers, the test is shown to be asymptotically optimal universally when the number of outliers is the largest possible and with the typical distribution being known, and its asymptotic performance otherwise is also characterized. An extension of the findings to the model with multiple distinct outliers is also discussed. In all cases, it is shown that the asymptotic performance guarantees for the proposed test when neither the outlier nor typical distribution is known converge to those when the typical distribution is known.
AB - Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are generated by an 'outlier' distribution, distinct from a common 'typical' distribution governing the majority of the sequences. Apart from being distinct, the outlier and typical distributions can be arbitrarily close. The goal is to design a universal test to best discern all the outlier sequences. A universal test with the flavor of the repeated significance test is proposed and its asymptotic performance is characterized under various universal settings. The proposed test is shown to be universally consistent. For the model with identical outliers, the test is shown to be asymptotically optimal universally when the number of outliers is the largest possible and with the typical distribution being known, and its asymptotic performance otherwise is also characterized. An extension of the findings to the model with multiple distinct outliers is also discussed. In all cases, it is shown that the asymptotic performance guarantees for the proposed test when neither the outlier nor typical distribution is known converge to those when the typical distribution is known.
UR - http://www.scopus.com/inward/record.url?scp=84940572548&partnerID=8YFLogxK
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U2 - 10.1109/ACSSC.2014.7094445
DO - 10.1109/ACSSC.2014.7094445
M3 - Conference contribution
AN - SCOPUS:84940572548
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 281
EP - 285
BT - Conference Record of the 48th Asilomar Conference on Signals, Systems and Computers
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 48th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
Y2 - 2 November 2014 through 5 November 2014
ER -