Graphical Nonconvex Optimization for Optimal Estimation in Gaussian Graphical Models
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimation in Gaussian graphical models, which is then approximated by a sequence of convex programs. Our proposal is computationally tractable and produces an estimator that achieves the oracle rate of convergence. The statistical error introduced by the sequential approximation using the convex programs are clearly demonstrated via a contraction property. The rate of convergence can be further improved using the notion of sparsity pattern. The proposed methodology is then extended to semiparametric graphical models. We show through numerical studies that the proposed estimator outperforms other popular methods for estimating Gaussian graphical models.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Graphical Nonconvex Optimization via an Adaptive Convex Relaxation
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracl…
Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimization
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the spars…
Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimizations
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse…
Nonconvex Sparse Graph Learning under Laplacian Constrained Graphical Model
In this paper, we consider the problem of learning a sparse graph from the Laplacian constrained Gaussian graphical model. This problem can be formulated as a penalized maximum likelihood estimation of the precision matr…
Graph LearningGraphical Convergence of Subgradients in Nonconvex Optimization and Learning
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the prima…
regressionStochastic Optimization