A note on the Lasso for Gaussian graphical model selection

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Structure Learning in Graphical Modeling (2016, background): “Indeed, there are Gaussian examples in which neighborhood selection is consistent whenever the glasso is consistent, but in which the converse is false (Meinshausen, 2008; Ravikumar et al., 2011).”
A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers (2009, methodology): “For generalized linear models (GLMs), estimators based on 1-regularized maximum likelihood have also been studied, including results on risk consistency [71], consistency in the 2 or 1-norm [2, 30, 44] and model selection consistency [9, 59].”