Related papers: Partial Correlation Graphical LASSO
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…
High dimensional Gaussian graphical models provide a rigorous framework to describe a network of statistical dependencies between entities, such as genes in genomic regulation studies or species in ecology. Penalized methods, including the…
Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…
We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes…
Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…
Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
In this paper, we propose a Bayesian Graphical LASSO for correlated countable data and apply it to spatial crime data. In the proposed model, we assume a Gaussian Graphical Model for the latent variables which dominate the potential risks…
We consider the problem of learning a coefficient vector x_0\in R^N from noisy linear observation y=Ax_0+w \in R^n. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator x'. In…
Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…