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Related papers: Positivity for Gaussian graphical models

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We consider multivariate centered Gaussian models for the random vector $(Z^1,\ldots, Z^p)$, whose conditional structure is described by a homogeneous graph and which is invariant under the action of a permutation subgroup. The following…

Statistics Theory · Mathematics 2022-09-22 Piotr Graczyk , Hideyuki Ishi , Bartosz Kołodziejek

We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…

Statistics Theory · Mathematics 2025-11-21 Stefan Tappe

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…

Methodology · Statistics 2017-03-07 Benjamin Frot , Luke Jostins , Gil McVean

Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…

Methodology · Statistics 2016-01-01 Kevin Lee , Lingzhou Xue

Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…

Machine Learning · Computer Science 2012-03-19 Bai Zhang , Yue Wang

Let $(Y,(X_i)_{i\in\mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of…

Statistics Theory · Mathematics 2008-05-23 Nicolas Verzelen , Fanny Villers

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…

Statistics Theory · Mathematics 2014-04-08 Sayantan Banerjee , Subhashis Ghosal

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…

Methodology · Statistics 2010-05-13 Julien Chiquet , Yves Grandvalet , Christophe Ambroise

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…

Data Structures and Algorithms · Computer Science 2023-11-10 Oliver E. Richardson , Joseph Y. Halpern , Christopher De Sa

We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…

Statistics Theory · Mathematics 2022-03-22 Sumanta Basu , Suhasini Subba Rao

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…

Methodology · Statistics 2018-08-21 Ginette Lafit , Francisco J. Nogales , Marcelo Ruiz , Ruben H. Zamar

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…

Machine Learning · Statistics 2014-04-30 Jianqing Fan , Han Liu , Yang Ning , Hui Zou

Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…

High Energy Physics - Theory · Physics 2008-11-26 Tomasz Konopka

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

Machine Learning · Statistics 2019-02-07 Zehang Richard Li , Tyler H. McCormick

Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…

Methodology · Statistics 2020-09-03 Irene Córdoba , Concha Bielza , Pedro Larrañaga

The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…

Methodology · Statistics 2025-04-11 Ching Wong , Giusi Moffa , Jack Kuipers

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

Methodology · Statistics 2015-03-19 Nanny Wermuth , Kayvan Sadeghi

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

Disordered Systems and Neural Networks · Physics 2025-11-17 Takashi Takahashi

Conditional Gaussian graphical models (cGGM) are a recent reparametrization of the multivariate linear regression model which explicitly exhibits $i)$ the partial covariances between the predictors and the responses, and $ii)$ the partial…

Methodology · Statistics 2014-09-26 Julien Chiquet , Tristan Mary-Huard , Stéphane Robin

In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…

Methodology · Statistics 2026-04-14 Michele Peruzzi