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Related papers: Positivity for Gaussian graphical models

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Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…

Quantitative Methods · Quantitative Biology 2017-04-13 Carlos Alberto Martínez , Kshitij Khare , Syed Rahman , Mauricio A. Elzo

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

Methodology · Statistics 2016-06-09 Mathias Drton , Marloes H. Maathuis

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

Methodology · Statistics 2015-10-12 Nanny Wermuth

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Statistics Theory · Mathematics 2007-06-13 Mathias Drton

Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…

Methodology · Statistics 2022-02-01 Jingfei Zhang , Yi Li

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…

Machine Learning · Statistics 2017-04-13 Janne Leppä-aho , Johan Pensar , Teemu Roos , Jukka Corander

We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for…

Methodology · Statistics 2020-03-23 Yuhao Wang , Uma Roy , Caroline Uhler

Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…

Statistics Theory · Mathematics 2013-10-30 Jan Draisma , Sonja Kuhnt , Piotr Zwiernik

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Computation · Statistics 2015-03-13 Sophie Donnet , Jean-Michel Marin

In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…

Methodology · Statistics 2019-07-26 Daniela De Canditiis , Armando Guardasole

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…

Machine Learning · Statistics 2016-11-22 Qinliang Su , Xuejun Liao , Chunyuan Li , Zhe Gan , Lawrence Carin

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…

Probability · Mathematics 2025-01-08 David Bolin , Alexandre B. Simas , Jonas Wallin

Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support…

Machine Learning · Statistics 2019-01-28 Ashish Katiyar , Jessica Hoffmann , Constantine Caramanis

We study a notion of positivity of Gaussian directed acyclic graphical models corresponding to a non-negativity constraint on the coefficients of the associated structural equation model. We prove that this constraint is equivalent to the…

Statistics Theory · Mathematics 2023-06-01 Asad Lodhia , Jan-Christian Hütter , Caroline Uhler , Piotr Zwiernik

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The…

Machine Learning · Statistics 2016-11-22 Qinliang Su , Xuejun Liao , Changyou Chen , Lawrence Carin

Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…

Statistics Theory · Mathematics 2015-05-08 Hao Wang

Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…

Methodology · Statistics 2021-04-08 Anna Gottard , Agnese Panzera

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Methodology · Statistics 2021-12-14 Eunice Okome Obiang , Pascal Jézéquel , Frédéric Proïa

Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…

Methodology · Statistics 2024-02-06 Sebastian Engelke , Manuel Hentschel , Michaël Lalancette , Frank Röttger

Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…

Applications · Statistics 2012-03-01 Jianxin Yin , Hongzhe Li