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SUMMARY:Fast low-rank estimation by projected gradient descent: Statistica
 l and algorithmic guarantees - Martin Wainwright (UC Berkeley)
DTSTART:20151120T160000Z
DTEND:20151120T170000Z
UID:TALK60702@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:Optimization problems with rank constraints arise in many\napp
 lications\, including matrix regression\, structured PCA\, matrix\ncomplet
 ion and matrix decomposition problems. An attractive heuristic\nfor solvin
 g such problems is to factorize the low-rank matrix\, and to\nrun projecte
 d gradient descent on the nonconvex problem in the lower\ndimensional fact
 orized space.  We provide a general set of conditions\nunder which project
 ed gradient descent\, when given a suitable\ninitialization\, converges ge
 ometrically to a statistically optimal\nsolution.  Our results are applica
 ble even when the initial solution\nis outside any region of local convexi
 ty\, and even when the problem is\nglobally concave.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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