Related papers: Partial Correlation Graphical LASSO
In a multivariate linear regression model with $p>1$ covariates, implementation of penalization techniques often implies a preliminary univariate standardization step. Although this prevents scale effects on the covariates selection…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm.…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
The graphical lasso (glasso) is a widely-used fast algorithm for estimating sparse inverse covariance matrices. The glasso solves an L1 penalized maximum likelihood problem and is available as an R library on CRAN. The output from the…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
We consider the problem of learning a high-dimensional graphical model in which certain hub nodes are highly-connected to many other nodes. Many authors have studied the use of an l1 penalty in order to learn a sparse graph in…
This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be…
Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
This paper proposes a penalized composite likelihood method for model selection in colored graphical Gaussian models. The method provides a sparse and symmetry-constrained estimator of the precision matrix, and thus conducts model selection…