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CATEGORIES:Probability Theory and Statistics in High and Infi
nite Dimensions
SUMMARY:On tensor completion via nuclear norm minimization
- Cun-Hui Zhang\, Rutgers University\, USA
DTSTART;TZID=Europe/London:20140625T144500
DTEND;TZID=Europe/London:20140625T151500
UID:TALK53117AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53117
DESCRIPTION:Many problems can be formulated as recovering a lo
w-rank tensor. Although an\nincreasingly common ta
sk\, tensor recovery remains a challenging problem
because\nof the delicacy associated with the deco
mposition of higher order tensors. To\novercome th
ese difficulties\, existing approaches often proce
ed by unfolding tensors\ninto matrices and then ap
ply techniques for matrix completion. We show here
that\nsuch matricization fails to exploit the ten
sor structure and may lead to suboptimal\nprocedur
e. More specifically\, we investigate a convex opt
imization approach to\ntensor completion by direct
ly minimizing a tensor nuclear norm and prove that
this\nleads to an improved sample size requiremen
t. To establish our results\, we develop\na series
of algebraic and probabilistic techniques such as
characterization of\nsubdifferetial for tensor nu
clear norm and concentration inequalities for tens
or\nmartingales\, which may be of independent inte
rests and could be useful in other\ntensor related
problems.\nJoint work with Ming Yuan.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
CONTACT:
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