We study the general class of estimators for graphical model structure based on optimizing ell_1-regularized approximate log-likelihood, where the approximate likelihood uses tractable variational approximations of the partition function. We provide a message-passing algorithm that directly computes the ell_1 regularized approximate MLE. Further, in the case of certain reweighted entropy approximations to the partition function, we show that surprisingly the ell_1 regularized approximate MLE estimator has a closed-form, so that we would no longer need to run through many iterations of approximate inference and message-passing. Lastly, we analyze this general class of estimators for graph structure recovery, or its sparsistency, and show that it is indeed sparsistent under certain conditions.

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In International Conference on Machine learning (ICML) 2011.

@inproceedings{YR11, title={On the Use of Variational Inference for Learning Discrete Graphical Models}, author={Eunho Yang and Pradeep Ravikumar}, booktitle={International Conference on Machine learning (ICML)}, series={28}, url="http://www.cs.utexas.edu/users/ai-lab?YR11", year={2011} }