Related papers: Estimation of Graphical Models using the $L_{1,2}$…
This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…
We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a more general penalty that blends the…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
Robots have been used in all sorts of automation, and yet the design of robots remains mainly a manual task. We seek to provide design tools to automate the design of robots themselves. An important challenge in robot design automation is…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
We develop a new method called Discriminated Hub Graphical Lasso (DHGL) based on Hub Graphical Lasso (HGL) by providing prior information of hubs. We apply this new method in two situations: with known hubs and without known hubs. Then we…
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…
The graph fused lasso -- which includes as a special case the one-dimensional fused lasso -- is widely used to reconstruct signals that are piecewise constant on a graph, meaning that nodes connected by an edge tend to have identical…
We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
We investigate the problem of estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model (GGM) on the network. In this vein, we consider GGMs whose covariance structures align with the geometry…
Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…
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…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…