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SUMMARY:Optimal Covariance Change Point Detection in High Dimension - Yi Y
 u (University of Cambridge\; University of Bristol)
DTSTART:20180118T090000Z
DTEND:20180118T094500Z
UID:TALK97801@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Daren Wang		(Carnegie Mellon University)\, Alessan
 dro Rinaldo		(Carnegie Mellon University)&nbsp\;<br><br>In this paper\, we
  study covariance change point detection problem in high dimension. Specif
 ically\, we assume that the time series&nbsp\; $X_i \\in \\mathbb{R}^p$\, 
 $i = 1\, \\ldots\, n$ are independent $p$-dimensional sub-Gaussian random 
 vectors and that the corresponding covariance matrices $\\{\\Sigma_i\\}_{i
 =1}^n$ are stationary within segments and only change at certain time poin
 ts.&nbsp\; Our generic model setting allows $p$ grows with $n$ and we do n
 ot place any additional structural assumptions on the covariance matrices.
 &nbsp\; We introduce algorithms based on binary segmentation (e.g. Vostrik
 ova\, 1981) and wild binary segmentation (Fryzlewicz\, 2014) and establish
  the consistency results under suitable conditions.&nbsp\; To improve the 
 detection performance in high dimension\, we propose&nbsp\; &nbsp\;Wild Bi
 nary Segmentation through Independent Projection (WBSIP).&nbsp\; We show t
 hat WBSIP can optimally estimate the locations of the change points.&nbsp\
 ; Our analysis also reveals a phase transition effect based on our generic
  model assumption and to the best of our knowledge\, this type of results 
 have not been established elsewhere in the change point detection literatu
 re.
LOCATION:Seminar Room 1\, Newton Institute
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