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DTSTART:20190310T070000
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DTSTART:20191103T060000
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UID:69f359eb342bf
DTSTART;TZID=America/Toronto:20200305T160000
SEQUENCE:0
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URL:https://uwaterloo.ca/statistics-and-actuarial-science/events/department
 -seminar-stilian-stoev-university-michigan
LOCATION:M3 - Mathematics 3 200 University Avenue West Room: 3127 Waterloo 
 ON N2L 3G1 Canada
SUMMARY:Department seminar by Stilian Stoev\, University of Michigan
CLASS:PUBLIC
DESCRIPTION:CONCENTRATION OF MAXIMA: FUNDAMENTAL LIMITS OF EXACT SUPPORT RE
 COVERY\nIN HIGH DIMENSIONS\n\nWe study the estimation of the support (set 
 of non-zero components) of\na sparse high-dimensional signal observed with
  additive and dependent\nnoise. With the usual parameterization of the siz
 e of the support set\nand the signal magnitude\, we characterize a phase-t
 ransition\nphenomenon akin to the Ingster’s signal detection boundary. 
  We\nshow that when the signal is above the so-called strong classificati
 on\nboundary\, thresholding estimators achieve asymptotically perfect\nsup
 port recovery. This is so under arbitrary error dependence\nassumptions\, 
 provided that the marginal error distribution has rapidly\nvarying tails. 
  Conversely\, under mild dependence conditions on the\nnoise\, we show th
 at no thresholding estimators can achieve perfect\nsupport recovery if the
  signal is below the boundary.  For\nlog-concave error densities\, the th
 resholding estimators are shown to\nbe optimal and hence the strong classi
 fication boundary is universal\,\nin this setting.\n\nThe proofs exploit a
  concentration of maxima phenomenon\, known as\nrelative stability. We obt
 ain a complete characterization of the\nrelative stability phenomenon for 
 dependent Gaussian noise via\nSlepian\, Sudakov-Fernique bounds and some R
 amsey theory.
DTSTAMP:20260430T133227Z
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