Robust Gaussian Graphical Modeling with the Trimmed Graphical Lasso
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs. Our method guards against outliers by an implicit trimming mechanism akin to the popular Least Trimmed Squares method used for linear regression. We provide a rigorous statistical analysis of our estimator in the high-dimensional setting. In contrast, existing approaches for robust sparse GGMs estimation lack statistical guarantees. Our theoretical results are complemented by experiments on simulated and real gene expression data which further demonstrate the value of our approach.
The paper presents a method for robust inference of sparse GGM models. Theoretical guarantees on estimated models are given even when these estimates correspond to merely local optima of the relevant objective function.The paper is clearly presented and organised logically: after introducing the problem to be solved the objective function (3) is presented. A reasonable approach to optimisation is presented - Algorithm 1. Since the objective is only bi-convex not convex no attempt is made to find a global minimum. Instead theoretical guarantees are given on *any* local minimum subject to certain conditions. Some work is done in Section 3 to provide the reader with some feeling for when these conditions will be met. Experiments with both synthetic and real data are provided.(3) is a reasonable way of dealing with outliers/noise and it is clearly good to have the theoretical guarantees. However, I found it hard to be convinced that much had been gained - for practical problems - over existing technqiues. (The authors deserve praise for comparing against a good selection of alternatives.) The results in Fig 1 show that the proposed method is indeed "competitive" but not superior by a large margin. On the other hand doing somewhat better than alternatives *and* having some theoretical guarantees is a contribution.Other points...Please mention that \tau_{1}, \tau_{2} and \tau are all defined in the supplementary material - I searched hard for their definitions in the main paper!I did not understand the sentence at line 236. What does it mean to choose a parameter "from [a] quantity"?51 paid on -> paid to 123 if i-th sample -> if the i-th sample 125 only small number -> only a small number 242 how easy we can satisfy -> how easily we can satisfy 277 Note that -> Note that the 278 Corollary 2 recover -> Corollary 2 reveals an 285 by arbitrary optimization -> by an arbitrary optimization286 multiple local optimum -> multiple local optima 291 from other -> from another365 Fix j subscript. Also is -> if 463 gaussian -> Gaussian