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

Philippe Rigollet rigollet at Princeton.EDU
Tue Sep 7 13:17:47 EDT 2010


Hi ml-stat-talks

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×m
matrix  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 M
approximation of  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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