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SUMMARY:Uniform pertubation analysis of eigenspaces and its applications t
 o Community Detection\, Ranking and Beyond - Jianqing Fan (Princeton Unive
 rsity)
DTSTART:20180115T141000Z
DTEND:20180115T145500Z
UID:TALK97573@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Emmanuel Abbe		(Princeton University)\, Kaiz
 heng Wang		(Princeton University)\, Yiqiao Zhong		(Princeton University)  
       <br></span><span><br>Spectral methods have been widely used for a la
 rge class of challenging problems\, ranging from top-K ranking via pairwis
 e comparisons\, community detection\, factor analysis\, among others.   An
 alyses of these spectral methods require super-norm perturbation analysis 
 of top eigenvectors.  This allows us to UNIFORMLY approximate elements in 
 eigenvectors  by linear functions of the observed random matrix that can b
 e analyzed further.  We first establish such an infinity-norm pertubation 
 bound for top eigenvectors and apply the idea to several challenging probl
 ems such as top-K ranking\, community detections\, Z_2-syncronization and 
 matrix completion.  We show that the spectral methods are indeed optimal f
 or these problems.  We illustrate these methods via simulations.</span>
LOCATION:Seminar Room 1\, Newton Institute
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