Sparse Covariance Selection via Robust Maximum Likelihood Estimation
Abstract
We address a problem of covariance selection, where we seek a tradeoff between a high likelihood against the number of nonzero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by the sum of absolute values of the elements of the inverse covariance matrix, and allow for imposing bounds on the condition number of the solution. The problem is directly amenable to now standard interiorpoint algorithms for convex optimization, but remains challenging due to its size. We first give some results on the theoretical computational complexity of the problem, by showing that a recent methodology for nonsmooth convex optimization due to Nesterov can be applied to this problem, to greatly improve on the complexity estimate given by interiorpoint algorithms. We then examine two practical algorithms aimed at solving largescale, noisy (hence dense) instances: one is based on a blockcoordinate descent approach, where columns and rows are updated sequentially, another applies a dual version of Nesterov's method.
 Publication:

arXiv eprints
 Pub Date:
 June 2005
 arXiv:
 arXiv:cs/0506023
 Bibcode:
 2005cs........6023B
 Keywords:

 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Computer Science  Artificial Intelligence;
 F.2.1;
 G.1.3;
 G.1.6;
 G.3;
 J.3
 EPrint:
 Submitted to NIPS 2005