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CATEGORIES:Statistics
SUMMARY:Distribution-Free Detection of Structured Anomalie
s: Permutation and Rank-Based Scans - Rui Castro (
Eindhoven)
DTSTART;TZID=Europe/London:20160212T160000
DTEND;TZID=Europe/London:20160212T170000
UID:TALK63643AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63643
DESCRIPTION:The scan statistic is by far the most popular meth
od for anomaly detection\, being popular in syndro
mic surveillance\, signal and image processing and
target detection based on sensor networks\, among
other applications. The use of scan statistics i
n such settings yields an hypothesis testing proce
dure\, where the null hypothesis corresponds to th
e absence of anomalous behavior. If the null dist
ribution is known calibration of such tests is rel
atively easy\, as it can be done by Monte-Carlo si
mulation. However\, when the null distribution is
unknown the story is less straightforward. We in
vestigate two procedures: (i) calibration by permu
tation and (ii) a rank-based scan test\, which is
distribution-free and less sensitive to outliers.
A further advantage of the rank-scan test is that
it requires only a one-time calibration for a giv
en data size making it computationally much more a
ppealing than the permutation-based test. In both
cases\, we quantify the performance loss with res
pect to an oracle scan test that knows the null di
stribution. We show that using one of these cali
bration procedures results in only a very small lo
ss of power in the context of a natural exponentia
l family. This includes for instance the classica
l normal location model\, popular in signal proces
sing\, and the Poisson model\, popular in syndromi
c surveillance. Numerical experiments further supp
ort our theory and results (joint work with Ery Ar
ias-Castro\, Meng Wang (UCSD) and Ervin Tánczos (T
U/e)).
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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