[Ml-stat-talks] Reminder. Tomorrow: Vladimir Kolchinskii - ORFE Colloquium - Tuesday Sept. 28 - 4:30

Philippe Rigollet rigollet at princeton.edu
Mon Sep 27 09:54:47 EDT 2010


Hi ml-stat-talks

This a reminder of Vladimir Koltchinskii's talk tomorrow in the ORFE  
colloquium.

On Tuesday September 28, Vladimir Koltchinskii from the School of  
Mathematics at Georgia Tech will be giving a talk at the ORFE  
colloquium. It will take place in Sherrerd Hall, room101 at 4:30pm.
Sparse matrix estimation (such as noisy matrix completion) is one of  
the hottest topics in statistical learning. If you are interested in  
leaning about the most topical tools from empirical processes theory,  
don't miss this talk.

Speaker: Vladimir Koltchinskii, Georgia Tech (School of mathematics)

When/where: Tuesday, September 28 at 4:30pm in Sherrerd Hall (room 101)

Title: Von Neumann Entropy Penalization in Low Rank Matrix Regression

Abstract: A problem of estimation of a large Hermitian nonnegatively  
definite m-by-m
matrix  M of unit trace based on i.i.d. observations
Y_j = tr(M*X_j) + e_j , j = 1, . . . , n,
where X_j are random Hermitian m × m matrices and {e_j} is a zero mean
random noise will be considered. This version of the problem is of  
importance
in quantum state tomography, but similar problems occur in many
areas (such as matrix completion, large covariance matrix estimation,  
etc).
Our approach is based on a penalized least squares method with  
complexity
penalty defined in terms of von Neumann entropy. We derived oracle  
inequalities
showing the dependence of the estimation error on the accuracy of
approximation of  M by low rank matrices.

Bio: Vladimir Koltchinskii is a Professor at the School of Mathematics  
at Georgia Tech. His research focuses on empirical processes and  
applications to statistics and machine learning. He has made  
significant contributions to the theory of empirical processes,  
especially local Rademacher complexities and has more recently been  
interested in sparse estimation of vectors, functions and matrices. He  
gave a lecture on "Oracle Inequalities in Empirical Risk Minimization  
and Sparse Recovery Problems" at the 2008 St. Flour probability summer  
school and his notes will be be available soon from Springer.

--
Philippe RIGOLLET
www.princeton.edu/~rigollet 	
  	



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