title: Learning Latent Variable Gaussian Graphical Model for Biomolecular Network with Low Sample Complexity.
abstract: Learning a Gaussian graphical model with latent variables is ill posed when there is insufficient sample complexity, thus having to be appropriately regularized. A common choice is convexℓ1plus nuclear norm to regularize the searching process. However, the best estimator performance is not always achieved with these additive convex regularizations, especially when the sample complexity is low. In this paper, we consider a concave additive regularization which does not require the strong irrepresentable condition. We use concave regularization to correct the intrinsic estimation biases from Lasso and nuclear penalty as well. We establish the proximity operators for our concave regularizations, respectively, which induces sparsity and low rankness. In addition, we extend our method to also allow the decomposition of fused structure-sparsity plus low rankness, providing a powerful tool for models with temporal information. Specifically, we develop a nontrivial modified alternating direction method of multipliers with at least local convergence. Finally, we use both synthetic and real data to validate the excellence of our method. In the application of reconstructing two-stage cancer networks, "the Warburg effect" can be revealed directly.
authors.affiliation: Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Yanbo
authors.identifier: 0000-0001-7997-434X
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Quan
authors.initials: Q
authors.lastname: Liu
authors.affiliation: Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Bo
authors.identifier: 0000-0002-0004-6733
authors.initials: B
authors.lastname: Yuan
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D049109:Cell Proliferation; D003196:Computer Graphics; D003198:Computer Simulation; D005189:False Positive Reactions; D015972:Gene Expression Regulation, Neoplastic; D053263:Gene Regulatory Networks; D006019:Glycolysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008175:Lung Neoplasms / Q000378:metabolism; D008390:Markov Chains; D015233:Models, Statistical; D009369:Neoplasms / Q000235:genetics / Q000378:metabolism* / Q000473:pathology*; D016011:Normal Distribution; D010363:Pattern Recognition, Automated; D012984:Software