Wednesday, 15:15 - 15:40 h, Room: H 2038

 

Defeng Sun
Finding the nearest correlation matrix of exact low rank via convex optimization

Coauthor: Weimin Miao

 

Abstract:
In this talk, we aim to find a nearest correlation matrix of exact low rank from n independent noisy observations of entries under a general sampling scheme. Since the nuclear norm (trace) of a correlation matrix is a constant, the widely used nuclear norm regularization technique can no longer be applied to achieve this goal in the noisy setting. Here, we propose a new convex optimization approach by using a linear regularization term based on the observation matrix to represent the rank information. This convex optimization problem can be easily written as an H-weighted least squares semidefinite programming problem, which can be efficiently solved, even for large-scale cases. Under certain conditions, we show that our approach possesses the rank consistency. We also provide non-asymptotic bounds on the estimation error.

 

Talk 1 of the invited session Wed.3.H 2038
"Conic and convex programming in statistics and signal processing IV" [...]
Cluster 4
"Conic programming" [...]

 

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