Sparse Matrix Graphical Models

L0 sparse graphical modeling

Graphical models are well established in providing compact conditional probability descriptions of complex multivariable interactions. In the Gaussian case, graphical models are determined by zeros in the precision or concentration matrix, i.e. the inverse of the covariance matrix. Hence, there has been much recent interest in sparse precision matrices in areas such as statistics, machine learn...

Edge detection in sparse Gaussian graphical models

Applications of the lasso and grouped lasso to the estimation of sparse graphical models

We propose several methods for estimating edge-sparse and nodesparse graphical models based on lasso and grouped lasso penalties. We develop efficient algorithms for fitting these models when the numbers of nodes and potential edges are large. We compare them to competing methods including the graphical lasso and SPACE (Peng, Wang, Zhou & Zhu 2008). Surprisingly, we find that for edge selection...

Learning Latent Variable Gaussian Graphical Models

Gaussian graphical models (GGM) have been widely used in many highdimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. In this paper, we focus on a family of latent variable Gaussian graphical model...

Theoretical performance limits for jointly sparse signals via graphical models

The compressed sensing (CS) framework has been proposed for efficient acquisition of sparse and compressible signals through incoherent measurements. In our recent work, we introduced a new concept of joint sparsity of a signal ensemble. For several specific joint sparsity models, we demonstrated distributed CS schemes. This paper considers joint sparsity via graphical models that link the spar...