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Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Applications · Statistics 2018-08-07 Donald R. Williams , Juho Piironen , Aki Vehtari , Philippe Rast

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

Statistics Theory · Mathematics 2021-02-18 Kyoungjae Lee , Xuan Cao

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

Methodology · Statistics 2025-01-24 Takahiro Onizuka , Shintaro Hashimoto

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…

Machine Learning · Statistics 2018-06-08 Tatjana Pavlenko , Felix Leopoldo Rios

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

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical…

Machine Learning · Statistics 2012-07-30 Han Liu , Fang Han , Ming Yuan , John Lafferty , Larry Wasserman

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…

Machine Learning · Statistics 2018-02-14 Junwei Lu , Mladen Kolar , Han Liu

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Methodology · Statistics 2015-05-05 Kshitij Khare , Bala Rajaratnam , Abhishek Saha

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Computation · Statistics 2012-03-19 Richard G. Everitt

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Methodology · Statistics 2019-07-04 Peyman Jalali , Kshitij Khare , George Michailidis

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…

Statistics Theory · Mathematics 2010-12-01 Rina Foygel , Mathias Drton

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

Machine Learning · Computer Science 2017-11-07 Rebecca E. Morrison , Ricardo Baptista , Youssef Marzouk

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

Machine Learning · Statistics 2025-04-24 Jiahe Lin , Yikai Zhang , George Michailidis

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Methodology · Statistics 2022-11-08 Bingjing Tang , Vinayak Rao

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Methodology · Statistics 2007-06-12 Helen Armstrong , Christopher K. Carter , Kevin F. Wong , Robert Kohn

Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high…

Machine Learning · Statistics 2009-03-05 Han Liu , John Lafferty , Larry Wasserman

The PC algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs. In Gaussian models, tests of conditional independence are typically based on Pearson correlations, and…

Statistics Theory · Mathematics 2012-07-03 Naftali Harris , Mathias Drton

Graphical models, used to express conditional dependence between random variables observed at various nodes, are used extensively in many fields such as genetics, neuroscience, and social network analysis. While most current statistical…

Methodology · Statistics 2022-10-25 Jiajing Niu , Boyoung Hur , John Absher , D. Andrew Brown