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SUMMARY:Sparse CCA: Statistical and Computational Limits - Chao Gao\, Yale
  University
DTSTART:20150306T160000Z
DTEND:20150306T170000Z
UID:TALK56949@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:I will introduce the problem of sparse canonical correlation a
 nalysis (sparse CCA). The first part of the talk will focus on the statist
 ical side. I will argue that sparse CCA has an intrinsic difference from t
 he well studied sparse PCA problem because of the presence of high-dimensi
 onal nuisance parameters\, namely\, the marginal covariance matrices. A so
 mewhat surprising result we derived shows that the minimax rate of sparse 
 CCA is independent of the structure of the marginal covariance matrices. T
 he second part of the talk will focus on the computational side. A novel a
 lgorithm is proposed to achieve the minimax rate adaptively under an extra
  sample size condition. I will present a computational lower bound argumen
 t to show that such condition is necessary for all polynomial-time algorit
 hms under the Planted Clique hypothesis. A novel reduction procedure is co
 nstructed in order that the lower bound is faithful to the Gaussianity of 
 the model. A byproduct of this argument also provides a computational lowe
 r bound for sparse PCA under Gaussian spiked covariance model.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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