Model selection in Gaussian graphical models: High-dimensional consistency of l1-regularized MLE. Export

@inproceedings{citeulike:5176595, abstract = {We consider the problem of estimating the graph structure associated with a GaussianMarkov random field (GMRF) from i.i.d. samples. We study the performance of study theperformance of the ℓ1-regularized maximum likelihood estimator in the high-dimensionalsetting, where the number of nodes in the graph p, the number of edges in the graph s andthe maximum node degree d, are allowed to grow as a function of the number of samplesn. Our main result provides sufficient conditions on (n, p, d) for the ℓ1-regularized MLEestimator to recover all the edges of the graph with high probability. Under some conditionson the model covariance, we show that model selection can be achieved for sample sizesn = (d2 log(p)), with the error decaying as O(exp(−c log(p))) for some constant c. Weillustrate our theoretical results via simulations and show good correspondences betweenthe theoretical predictions and behavior in simulations.}, author = {Ravikumar, P. and Wainwright, M. J. and Raskutti, G. and Yu, B.}, citeulike-article-id = {5176595}, journal = {NIPS}, keywords = {gm, graphical\_model, model\_selection}, posted-at = {2009-07-16 10:30:28}, priority = {4}, title = {Model selection in Gaussian graphical models: High-dimensional consistency of l1-regularized MLE.}, year = {2008} }

TY - CONF ID - citeulike:5176595 L3 - citeulike-article-id:5176595 N2 - We consider the problem of estimating the graph structure associated with a GaussianMarkov random field (GMRF) from i.i.d. samples. We study the performance of study theperformance of the ℓ1-regularized maximum likelihood estimator in the high-dimensionalsetting, where the number of nodes in the graph p, the number of edges in the graph s andthe maximum node degree d, are allowed to grow as a function of the number of samplesn. Our main result provides sufficient conditions on (n, p, d) for the ℓ1-regularized MLEestimator to recover all the edges of the graph with high probability. Under some conditionson the model covariance, we show that model selection can be achieved for sample sizesn = (d2 log(p)), with the error decaying as O(exp(−c log(p))) for some constant c. Weillustrate our theoretical results via simulations and show good correspondences betweenthe theoretical predictions and behavior in simulations. JF - NIPS TI - Model selection in Gaussian graphical models: High-dimensional consistency of l1-regularized MLE. KW - gm KW - graphical_model KW - model_selection AU - Ravikumar, P AU - Wainwright, MJ AU - Raskutti, G AU - Yu, B PY - 2008/// ER -