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Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…
Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks compared to classical methods, mainly due to the limitations of the commonly used message-passing principle. Notably, their…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a lattice. To tackle this issue, a neighborhood selection procedure has been recently introduced. This procedure amounts to selecting a…
We consider estimation of undirected Gaussian graphical models and inverse covariances in high-dimensional scenarios by penalizing the corresponding precision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (Graphical Ridge)…
Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…
Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…
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…
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…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…
The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…
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…
Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…