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CATEGORIES:Statistics
SUMMARY:Sparse CCA: Statistical and Computational Limits -
Chao Gao\, Yale University
DTSTART;TZID=Europe/London:20150306T160000
DTEND;TZID=Europe/London:20150306T170000
UID:TALK56949AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56949
DESCRIPTION:I will introduce the problem of sparse canonical c
orrelation analysis (sparse CCA). The first part o
f the talk will focus on the statistical side. I w
ill argue that sparse CCA has an intrinsic differe
nce from the well studied sparse PCA problem becau
se of the presence of high-dimensional nuisance pa
rameters\, namely\, the marginal covariance matric
es. A somewhat surprising result we derived shows
that the minimax rate of sparse CCA is independent
of the structure of the marginal covariance matri
ces. The second part of the talk will focus on the
computational side. A novel algorithm is proposed
to achieve the minimax rate adaptively under an e
xtra sample size condition. I will present a compu
tational lower bound argument to show that such co
ndition is necessary for all polynomial-time algor
ithms under the Planted Clique hypothesis. A novel
reduction procedure is constructed in order that
the lower bound is faithful to the Gaussianity of
the model. A byproduct of this argument also provi
des a computational lower bound for sparse PCA und
er Gaussian spiked covariance model.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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