Tuo Zhao, Kathryn Roeder, Han Liu
Many statistical methods gain robustness and exibility by sacricing convenient computational structure. In this paper, we illustrate this fundamental tradeoff by studying a semiparametric graphical model estimation problem. We explain how new computational techniques help to solve this type of problem. In particularly, we propose a smooth-projected neighborhood pursuit method for efciently estimating high dimensional nonparanormal graphs with theoretical guarantees. Besides new computational and theoretical analysis, we also provide an alternative view to analyze the tradeoff between computational efciency and statistical error under a smoothing optimization framework. We also report experimental results on text and stock datasets.